The relationship between foot-ball impact with kick outcome

THE RELATIONSHIP BETWEEN FOOT-BALL IMPACT

AND KICK OUTCOME IN FOOTBALL KICKING

Submitted to

College of Sport and Exercise Science

VICTORIA UNIVERSITY

In fulfilment of the requirements for the degree

DOCTOR OF PHILOSOPHY

By

JAMES PEACOCK

2018

Principal supervisor: Dr. Kevin Ball

Associate supervisor: Dr. Simon Taylor

I

Abstract

Across the football codes, kicking is the main skill used to score goals and pass between team

members. Kicking with high ball velocity and high accuracy is required to kick to targets at far

distances or reach a submaximal target in less time. The impact phase is the most important

component of the kicking action: it is the only time a player forcefully contacts the ball to produce

the flight path. Ensuring high impact efficiency and the appropriate combination of flight

characteristics are imparted onto the ball during foot-ball impact is important for successful

kicking. The aim of this thesis was to determine how foot-ball impact characteristics influences

impact efficiency, ankle plantarflexion, ball flight characteristics and kicking accuracy. By using

a mechanical kicking machine to systematically explore impact characteristics and performing an

intra-individual analysis of human kickers, high-speed-video analysis of foot-ball impact found

impact characteristics influenced impact efficiency, ankle plantarflexion, ball flight

characteristics, and kicking accuracy. Increasing ankle joint stiffness, impact locations on the foot

closer to the ankle joint, altering foot-ball angle and reducing foot velocity each increased impact

efficiency. These results supported the coaching cue ‘maintaining a firm ankle’ during impact as

effective at increasing impact efficiency. The impact location between the foot and ball across the

medial-lateral direction, foot-ball angle and foot trajectory were each identified as influential to

ball flight characteristics and/ or kicking accuracy. The oblique impact theory applied to the

duration of impact provided a theoretical framework underpinning how each impact characteristic

influenced ball flight characteristics. More consistent performing players produced less kick-to-

kick variability in their impact characteristics, while lower kick accuracy was due to errors

produced in the combination of impact characteristics. In conclusion, foot-ball impact

characteristics were influential to impact efficiency, ankle plantarflexion, ball flight

characteristics, and kicking accuracy.

II

Student declaration

I, James Peacock, declare that the PhD thesis entitled The relationship between foot-ball impact

with kick outcome in football kicking is no more than 100,000 words in length including quotes

and exclusive of tables, figures, appendices, bibliography, references and footnotes. This thesis

contains no material that has been submitted previously, in whole or in part, for the award of any

other academic degree or diploma. Except where otherwise indicated, this thesis is my own work.

Signature: Date: 02/03/2018

III

Acknowledgements

Firstly, I would like to give a big thank-you to my principle supervisor, Kevin Ball. Kev, it’s been

a great pleasure to learn from you over the past five-ish years. The CPD placement, honours

degree, and PhD; thank you. You have provided many opportunities for me to grow as a researcher

and teacher.

I would also like to thank the contribution of Simon Taylor, my associate supervisor. Simon,

thank you for the opportunities and support you have provided, allowing me to grow as a

researcher and teacher.

A big thank you to Mick Kusel and Robert Stokes for your contributions to the development of

the mechanical kicking machine. The mechanical kicking machine is one of the foundations of

this thesis, and your contributions to it cannot be put into words. Thank you.

I would also like to thank Brandon Defina, Caleb Brockwell and Ross Brown for their

contributions as research assistant’s. Guys, you contributed heaps to this thesis. You put in hours

of work helping me collect data and problem solve camera setups. I hope my work as a supervisor

was of benefit to you guys!

Thank you, Ketha, for passing on a little bit of your expansive knowledge of photography. Your

expertise not only helped with setting up the cameras to collect great data, but also helped with

my personal joy and development of nature photography.

A big thank-you to the fellow PhD students in biomechanics – Ale, Steph, Suus and Soheil. It’s

been a great past few years, and some very memorable celebrations while at conferences.

Lastly, a massive thank you to Abbey and my parents. Abbey (my wife), you’ve only known me

while I have been studying/ completing my research degrees. Thank you for your support

throughout the years, and now we can transition into post-PhD life. My parents, thank you also

for your support throughout my university degrees. From not paying rent and contributing little

to household chores, it made the years of my undergraduate, honours and first few years of PhD

degrees a breeze! Also thanks to my sisters.

IV

Contents

Abstract ............................................................................................................................ I

Student declaration ....................................................................................................... II

Acknowledgements ....................................................................................................... III

Contents ......................................................................................................................... IV

List of Figures ............................................................................................................... XI

List of Tables ............................................................................................................. XVII

Chapter 1 : Introduction ................................................................................................ 1

1.1. Aims .......................................................................................................................... 6

1.2. Thesis structure ......................................................................................................... 9

Chapter 2 : Literature review...................................................................................... 11

2.1. The generation of ball velocity ................................................................................ 11

2.1.1 Theoretical framework ................................................................................. 11

2.1.2 Foot velocity ................................................................................................. 15

2.1.3 Impact efficiency .......................................................................................... 19

2.1.4 Summary of factors influential to ball velocity ............................................ 26

2.2. Kicking accuracy ..................................................................................................... 27

2.2.1 Theoretical framework ................................................................................. 27

2.2.2 The ball flight path ....................................................................................... 30

2.2.3 The relationship between foot-ball impact characteristics with ball flight

characteristics ........................................................................................................ 32

2.2.4 Other factors influencing kicking accuracy .................................................. 34

V

2.2.5 Summary of factors influencing kicking accuracy ....................................... 37

2.3. Methodological approaches to analysing foot-ball impact ...................................... 38

2.3.1 Analysis of human kickers ........................................................................... 38

2.3.2 Mechanical kicking machines ...................................................................... 39

2.3.3 Theoretical models & computer simulations ................................................ 39

Chapter 3 : Study 1 - The impact phase of drop punt kicking: validation and

experimental data of a mechanical kicking limb ....................................................... 41

3.1. Introduction ............................................................................................................. 42

3.2. Methods ................................................................................................................... 43

3.3. Results ..................................................................................................................... 44

3.4. Discussion ............................................................................................................... 44

3.5. Conclusions ............................................................................................................. 47

3.6. Acknowledgements ................................................................................................. 47

3.7. Contribution of individual chapter to overall thesis ................................................ 47

Chapter 4 : Study 2 - The relationship between foot-ball impact and flight

characteristics in punt kicking .................................................................................... 48

4.1. Introduction ............................................................................................................. 50

4.2. Methods ................................................................................................................... 52

4.3. Results ..................................................................................................................... 58

VI

4.4. Discussion ............................................................................................................... 62

4.4.1 Foot velocity ................................................................................................. 62

4.4.2 Impact location ............................................................................................. 65

4.4.3 Ball orientation about the x-axis ................................................................... 66

4.5. Conclusion............................................................................................................... 67


Chapter 5 : Study 3 - The influence of joint rigidity on impact efficiency and ball

velocity in football kicking ........................................................................................... 69

5.1. Introduction ............................................................................................................. 70

5.2. Methods ................................................................................................................... 72

5.2.1 Mechanical kicking machine with adjustable ankle rigidity ........................ 72

5.2.2 The initial conditions of impact for the comparison of ankle rigidity .......... 74

5.2.3 Data collection .............................................................................................. 74

5.2.4 Data analysis and parameter calculation ...................................................... 75

5.2.5 Statistical analysis ........................................................................................ 78

5.3. Results ..................................................................................................................... 78

5.3.1 Validation of mechanical limb segment ....................................................... 78

5.3.2 Comparison of ankle rigidity settings ........................................................... 79

5.4. Discussion ............................................................................................................... 81

5.4.1 Validation of non-rigid ankle limb configuration ......................................... 81

5.4.2 Comparison of rigid to non-rigid ankle ........................................................ 81

5.5. Conclusion............................................................................................................... 83


Chapter 6 : Study 4 - Strategies to improve impact efficiency in football kicking . 85

VII

6.1. Introduction ............................................................................................................. 86

6.2. Methods ................................................................................................................... 88

6.2.1 Mechanical kicking machine ........................................................................ 88

6.2.2 Data collection and analysis ......................................................................... 89

6.2.3 Statistical analysis ........................................................................................ 93

6.3. Results ..................................................................................................................... 94

6.3.1 The influence of foot velocity ...................................................................... 94

6.3.2 The influence of impact location .................................................................. 94

6.3.3 The influence of joint stiffness ..................................................................... 95

6.4. Discussion and implications .................................................................................... 96

6.4.1 The influence of foot velocity ...................................................................... 96

6.4.2 The influence of impact location .................................................................. 97

6.4.3 The influence of joint stiffness ................................................................... 100

6.4.4 Practical applications .................................................................................. 102

6.5. Conclusion............................................................................................................. 103

6.6. Contribution of individual chapter to overall thesis .............................................. 104

Chapter 7 : Study 5 - Is there a sweet spot on the foot in kicking? ........................ 105

7.1. Introduction ........................................................................................................... 106

7.2. Methods ................................................................................................................. 108

7.2.1 Task, data collection and analysis .............................................................. 108

7.2.2 Calculation of impact point ........................................................................ 111

7.2.3 Statistical analysis ...................................................................................... 112

7.3. Results ................................................................................................................... 114

7.3.1 Validation of impact location measurement ............................................... 114

7.3.2 The distribution of impact locations between kicks. .................................. 115

VIII

7.3.3 The relationship between impact location and kick outcome. .................... 117

7.4. Discussion ............................................................................................................. 124

7.4.1 Did players target a specific location on their foot? ................................... 124

7.4.2 Medial-lateral impact location .................................................................... 124

7.4.3 Proximal-distal impact location .................................................................. 125

7.4.4 Is there a sweet spot on the foot? ................................................................ 128

7.5. Conclusion............................................................................................................. 129


Chapter 8 : Study 6 - Kick impact characteristics of accurate football kicking ... 130

8.1. Introduction ........................................................................................................... 132

8.2. Methods ................................................................................................................. 135

8.2.1 Task, data collection and analysis .............................................................. 135

8.2.2 Statistical analysis ...................................................................................... 141

8.3. Results ................................................................................................................... 142

8.4. Discussion ............................................................................................................. 147

8.4.1 Biomechanical factors explaining kicking accuracy .................................. 148

8.4.2 The influence of variability on kicking accuracy ....................................... 150

8.4.3 General discussion ...................................................................................... 151

8.5. Conclusion............................................................................................................. 153


Chapter 9 : Study 7 - The contact area between foot and ball during impact ...... 155

9.1. Introduction ........................................................................................................... 156

IX

9.2. Methods ................................................................................................................. 157

9.2.1 Data collection ............................................................................................ 158

9.2.2 Deformation of an ellipsoidal ball and calculation of impact location ....... 159

9.2.3 Parameter calculation ................................................................................. 164

9.3. Results ................................................................................................................... 165

9.4. Discussion ............................................................................................................. 167

9.5. Conclusion............................................................................................................. 175


Chapter 10 : General discussion ............................................................................... 176

10.1. How do foot-ball impact characteristics influence impact efficiency and ankle

plantarflexion ............................................................................................................... 176

10.1.1 The influence of foot-ball impact characteristics on impact efficiency.... 176

10.1.2 Does reducing change in ankle plantarflexion during foot-ball impact

influence impact efficiency?................................................................................ 188

10.1.3 Limitations and future directions to increase impact efficiency ............... 192

10.2. How do foot-ball impact characteristics influence ball flight characteristics and

kicking accuracy........................................................................................................... 194

10.2.1 The influence of foot-ball impact characteristics on ball flight

characteristics and kicking accuracy ................................................................... 194

10.2.2 Why players produce inaccurate kicks: a new theory defining human

kicking accuracy .................................................................................................. 201

10.2.3 Strategies to improve kicking accuracy .................................................... 204

10.2.4 Limitations and future directions to improve kicking accuracy ............... 207

10.3. Differences between mechanical kicking machine and the human kicking limb 209

10.3.1 Impact characteristics of the mechanical kicking machine and the human

kicking limb ......................................................................................................... 209

X

10.3.2 Smoothing procedures for the mechanical kicking machine and the human

kickers ................................................................................................................. 214

10.4. Transfer of knowledge between kicking styles ................................................... 216

Chapter 11 : Conclusion ............................................................................................ 217

Chapter 12 : References ............................................................................................. 220

Appendix A: Published manuscript of Study 1 ..................................................... 226

Appendix B: Published manuscript of Study 2 ..................................................... 230

Appendix C: Published manuscript of Study 3 ..................................................... 241

XI

List of Figures

Figure 2.1: Measurements of kicking accuracy as a two-dimensional coordinate in the vertical

plane when scoring (A) and passing (B) in different codes of football. The direction of

the coordinates is represented by the red arrows. ........................................................... 28

Figure 2.2: Ball flight characteristics .......................................................................................... 30

Figure 3.1: Correlations between foot speed with ball speed (A), F:B ratio (B, black round ticks,

primary axis) and COR (B, grey square ticks, secondary axis). .................................... 44

Figure 4.1: The mechanical limb ................................................................................................. 53

Figure 4.2: Foot segment attached at the distal point of shank ................................................... 53

Figure 4.3: Reflective and virtual markers attached to the limb and ball .................................... 54

Figure 4.4: Orthogonal reference system, approximate location of fCOM virtual marker and

parameter calculation of impact location on the foot, elevation angle and azimuth angle.

Arrows and angles represent positive directions. ........................................................... 56

Figure 4.5: The relationships between foot velocity with ball velocity (A), azimuth angle (B),

elevation angle (C), back-spin rate (D), foot-ball speed ratio (E), and the coefficient of

restitution (F). ................................................................................................................. 59

Figure 4.6: The relationships between impact location across the medial-lateral direction with ball

velocity (A), azimuth angle (B), elevation angle (C), and back-spin rate (D). .............. 60

Figure 4.7: The relationships between impact location across the proximal-distal direction with

ball velocity (A), azimuth angle (B), elevation angle (C), and back-spin rate (D). ....... 61

Figure 4.8: The relationships between ball orientation about the x-axis with ball velocity (A),

azimuth angle (B), elevation angle (C), and back-spin rate (D). .................................... 62

XII

Figure 4.9: Post-hoc analysis of the relationship between foot velocity with ball velocity. The

solid line represents the linear curve, and the dashed line represents the power curve.. 63

Figure 5.1: A) The mechanical kicking limb. B) Ankle rotation design with controlled rigidity via

spring mechanism........................................................................................................... 72

Figure 5.2: Orthogonal reference and tracking and virtual markers of the limb and ball. Virtual

markers are represented by the grey outline of the circular markers. ............................ 76

Figure 5.3: Non-rigid ankle motion through impact (± standard deviation). The flat black line

represents ankle angle at impact start, plotted throughout the duration of impact as a

reference to the change in angle during impact. ............................................................. 79

Figure 6.1: Mechanical kicking machine (A) and limb with rotation about the ankle (B). ........ 89

Figure 6.2: Reflective tracking markers and key anatomical landmarks. ................................... 91

Figure 6.3: Video overlay of foot model (solid line) and ball model (dashed line) at ball contact.

Figure A identifies when the foot and ball models were not in contact at visually identified

ball contact, as depicted by the foot model being to the left of the ball model. Image B

identifies when the ball was partially deformed at ball contact, as depicted by the foot

model being to the right of the ball model. .................................................................... 93

Figure 6.4: The relationship between foot velocity and ankle plantarflexion (A); the relationship

between foot velocity and ball velocity (B). Impact location was held constant at 0.4 cm

and joint stiffness was held constant at 1118 N. ............................................................ 94

Figure 6.5: The relationship between proximal-distal impact location and ankle plantarflexion

(B); the relationship between proximal-distal impact location and ball velocity (B). Foot

velocity was held constant at 16.5 m/s and joint stiffness was held constant at 1118 N.

........................................................................................................................................ 95

XIII

Figure 6.6: The relationship between joint stiffness and ankle plantarflexion (A); the relationship

between joint stiffness and ball velocity (B). Impact location was held constant at 0.4 cm

and foot velocity was held constant at 16.5 m/s. ............................................................ 95

Figure 6.7: Post-hoc analysis of ankle plantarflexion for two trials from the low (solid line) and

high (dashed line) foot velocities through impact. Each plotted line was comparable to

other trials in their respective groups. ............................................................................ 96

Figure 6.8: Post-hoc analysis of ankle plantarflexion for two trials from the proximal (dashed line)

and distal (solid line) impact locations. Each plotted line was comparable to other trials

in their respective groups. .............................................................................................. 98

Figure 7.1: A) the grid representing the anterior aspect of the foot. B) the model of the ball shell.

Approximate locations of static markers are attached to the foot. ............................... 112

Figure 7.2: The impact location for Player 4. A) Histogram of impact location across the proximal-

distal impact location (cm from foot centre of mass). B) Histogram of impact location

across the medial-lateral impact location (cm from foot centre of mass). The bivariate

distribution plot has been superimposed onto the foot, and the scale (C) represents the

relative distribution. ..................................................................................................... 116

Figure 7.3: The relationship between medial-lateral impact location and azimuth ball flight angle

for Player 8. The sweet spot location (the point on the horizontal axis) can be identified

by identifying the azimuth ball flight angle (vertical axis at 0°) from the regression line.

Positive values represent the lateral direction from foot centre (impact location) and ball

flight trajectory (azimuth ball flight angle). ................................................................. 118

Figure 7.4: The proximal-distal (P-D) sweet spot locations for Player 4, as identified by the

quadratic regressions between impact location with foot-ball speed ratio (FB Ratio),

coefficient of restitution (COR), and effective mass (EM). Positive values of impact

location represent the distal location from the foot centre. .......................................... 118

XIV

Figure 8.1: Visual representation of ball flight characteristics. A) Ball flight trajectory. B) Ball

angular dimensions. ...................................................................................................... 137

Figure 8.2: Surface models of the foot (A) and ball (B). .......................................................... 140

Figure 8.3: Measurement of ball impact location across the elevation plane (A) and the azimuth

plane (B). ...................................................................................................................... 140

Figure 9.1: Orthogonal reference and tracking and virtual markers of the limb and ball. Virtual

markers are represented by the grey outline of the circular markers. .......................... 159

Figure 9.2: Location of landmarks ............................................................................................ 160

Figure 9.3: Representation of foot and ball model .................................................................... 161

Figure 9.4: Foot and ball model, 25 frames into contact (near the point of maximal deformation).

The points ILx,y and PSx,y represent the x-y coordinates of the impact location on the

foot and the maximum displacement between the foot and ball shell in the perpendicular

direction, respectively. The solid linear line between the points ShBx,y and FBx,y

represent the dorsal aspect of the foot and the dotted linear line between the points ILx,y

and PSx,y is the deformation distance. All other points have been previously defined.

...................................................................................................................................... 164

Figure 9.5: The profile of impact. Foot velocity (solid black line; primary axis), ball velocity (grey

line; primary axis) and ball deformation (dashed black line; secondary axis) through the

duration of impact. ....................................................................................................... 165

Figure 9.6: Ball orientation (solid black line; primary axis) and impact location (dashed black

line; secondary axis). .................................................................................................... 166

XV

Figure 9.7: Ball deformation and corresponding video images at five points in time for one

particular trial. Images A and E are the immediate frame prior to ball contact (B) and after

ball release (E).............................................................................................................. 167

Figure 9.8: Ball angular velocity during impact (mean = black line; standard deviation = grey

lines). ............................................................................................................................ 171

Figure 9.9: Change in foot surface – ball long axis orientation during impact. Comparisons are

provided at the instance of ball contact (A) and approximately three-fourths of impact

duration (frame 30 of 44) (B). ...................................................................................... 172

Figure 9.10: A snapshot at foot-ball contact when ball angular velocity was 0°/s because the foot

surface and ball long axis were parallel (Chapter 4.4.3 Ball orientation about the x-axis).

...................................................................................................................................... 172

Figure 9.11: Estimation of force direction from ball deformation acting perpendicular to the foot

surface. ......................................................................................................................... 173

Figure 10.1: The relationship between ball orientation and kinetic energy (both translational and

rotational) for the mechanical kicking machine. .......................................................... 180

Figure 10.2: foot-ball angle that produced highest kinetic energy for the mechanical kicking

machine (A) and the foot-ball angle commonly used in drop punt kicking (B). .......... 181

Figure 10.3: Ankle plantar/dorsal flexion of three kicks that underwent a total change in ankle

angle of less than 1°. .................................................................................................... 186

Figure 10.4: Theoretical analysis of the relationship between proximal-distal impact location and

foot-ball speed ratio in response to increasing the stiffness of the muscle tendon unit. Line

A represents the untrained ankle. Line B represents an increase foot-ball speed ratio due

to reduced ankle motion during foot-ball impact. Line C represents an increase in the

XVI

‘power zone’, whereby a stronger muscle tendon unit may allow for greater end-point

variability in impact location. ...................................................................................... 187

Figure 10.5: A greater slope is anticipated for a narrower foot, because the change in surface angle

occurs over a shorter linear distance. ........................................................................... 212

XVII

List of Tables

Table 3.1: Summary of impact characteristics across the literature of AF kicking..................... 45

Table 5.1: Kick impact characteristics. ....................................................................................... 80

Table 7.1: Characteristics of individual players. ....................................................................... 109

Table 7.2: The mean and standard deviations of impact locations across the medial-lateral and

proximal-distal directions of the foot, measured from the foot centre. Positive values

represent the lateral and distal direction of the foot. .................................................... 115

Table 7.3: Relationship between medial-lateral impact location and azimuth ball flight angle.

...................................................................................................................................... 117

Table 7.4: Relationship between proximal-distal impact location and change in ankle

plantar/dorsal flexion. .................................................................................................. 120

Table 7.5: Relationship between proximal-distal impact location and foot-ball speed ratio. ... 121

Table 7.6: Relationship between proximal-distal impact location and effective mass. ............ 122

Table 7.7: The relationship between proximal-distal impact location and coefficient of restitution.

...................................................................................................................................... 123

Table 8.1: The descriptive statistics of kicking accuracy and ball flight characteristics (N = 114).

...................................................................................................................................... 142

Table 8.2: Regression results of ball flight characteristics predicting kicking accuracy (N = 114).

...................................................................................................................................... 143

Table 8.3: The mean and standard deviation of azimuth ball flight angle and kicking

characteristics for all individuals. ................................................................................. 144

XVIII

Table 8.4: Regression results of foot-ball impact characteristics predicting azimuth ball flight

trajectory. The coefficient (B), standard error (σe) and standardised coefficients (β) of

statistically significant (p < 0.05) foot-ball impact characteristics predicting azimuth ball

flight trajectory. Foot-ball angle Z was entered into the regression; however, this

parameter was statistically non-significant and omitted from the table. ...................... 145

Table 8.5: The standard deviations of azimuth ball flight trajectory, azimuth ball impact location,

and foot-ball angle Y for each player, ranked from lowest to highest using azimuth ball

flight trajectory as the performance indicator. ............................................................. 147

Table 10.1: Correlation (r) between ankle dorsiflexion angle at impact start and change in ankle

plantarflexion; correlation (r) between ankle dorsiflexion angle at impact start and change

in ankle plantarflexion partial to impact location across the proximal-distal direction on

the foot. ........................................................................................................................ 183

Table 10.2: Multiple linear regression results predicting the vertical component of kicking

accuracy. This regression was performed using the same methods and dataset from

Chapter 8. ..................................................................................................................... 195

Table 10.3: Bivariate regressions of the relationship between foot elevation trajectory and ball

elevation angle. ............................................................................................................ 198

Table 10.4: Comparisons of foot-ball impact characteristics from kicks with different task

constraints; indicating how players might functionally vary to satisfy different task

constraints. ................................................................................................................... 203

Table 10.5: Numerical representation of relationship between medial-lateral impact location with

azimuth ball flight trajectory and the relationship between azimuth ball impact location

with azimuth ball flight trajectory. ............................................................................... 210

Chapter 1: Introduction

Kicking is the defining skill of the football codes. In each of the football codes, kicking

is one of the most common modes of disposal used to score goals, to pass to fellow team members,

and to clear the ball from defensive pressure. The execution of the kicking skill varies between

and within each football code due to the constraints imposed during gameplay, but the

fundamental movement pattern of the skill is consistent: players swing their striking limb forward,

impact the ball with their foot, and impart a combination of ball flight characteristics.

There are two demands that players must meet for kicks to be successful within gameplay:

high accuracy and high ball velocity. High kicking accuracy is required to successfully score

goals/ points and pass to fellow team members, and is achieved by imparting a combination of

flight characteristics that ensures the ball passes within a set area of space such as the goal posts

or within receiving distance of the desired team member when passing. Kicking with a higher ball

velocity will provide more opportunities to pass and score, as targets that are further in distance

from the kicker can be reached. Kicking with a high ball velocity when passing and scoring at

submaximal distances is also desirable within gameplay: with a higher ball velocity and a reduced

elevation angle, the ball will travel a set distance in a shorter time, limiting the opportunity for

opposition players to intercept the ball. The ability to kick with both high ball velocity and high

accuracy is desirable for skilled players of all football codes, and understanding how players attain

these two characteristics is important for performance.

Most biomechanical research of football kicking has explored how players attain a high

ball velocity. Foot velocity has consistently been identified as an important factor toward final

ball velocity and the ultimate kick distance (Andersen, Dörge, & Thomsen, 1999; Ball, 2008a;

Dørge, Andersen, Sørensen, & Simonsen, 2002; Ishii, Yanagiya, Naito, Katamoto, & Maruyama,

2012; Nunome, Lake, Georgakis, & Stergioulas, 2006b). Researchers have consequently

identified the factors that influence foot velocity, whereby the coordination pattern can be

summarised as a proximal-distal sequence. The final step length, the magnitude of hip extension

2

at the top of the back swing, the knee extension muscular work during the forward swing, and the

knee extension angular velocity just prior to impact are each important components in producing

a high foot velocity (Ball, 2011; Dørge, et al., 2002; Nunome, Asai, Ikegami, & Sakurai, 2002;

Nunome, Ikegami, Kozakai, Apriantono, & Sano, 2006a). The importance of foot velocity toward

ball velocity also has theoretical support: the conservation of momentum combined with the

coefficient of restitution (Equation 1.1), a theoretical equation representing the collision between

foot and ball, identifies foot velocity and impact efficiency measures of foot-ball speed ratio,

effective mass and coefficient of restitution will determine final ball velocity.

𝑣𝑏 = (

1 + 𝑒

1 + 𝑚𝑏 𝑚𝑓⁄) ∙ 𝑢𝑓 + (

𝑒 − 𝑚𝑏 𝑚𝑓⁄

1 + 𝑚𝑏 𝑚𝑓⁄) ∙ 𝑢𝑏 Equation 1.1

Where vb = ball velocity after it leaves the foot, e = coefficient of restitution, mb = ball

mass, mf = foot mass, uf = initial foot velocity, ub = initial ball velocity.

Impacting the ball efficiently is required to impart a high ball velocity for a given foot

velocity. While a player can alter their biomechanics to increase foot velocity, it is important they

impact the ball appropriately to ensure efficient transfer of energy. Foot-ball impact lasts

approximately 7-16 ms between different kicking styles (Ball, 2010; Peacock, Ball, & Taylor,

2017a; Shinkai, Nunome, Isokawa, & Ikegami, 2009; Shinkai, Nunome, Suito, Inoue, & Ikegami,

2013; Tsaousidis & Zatsiorsky, 1996), and energy is transferred from foot to ball (Shinkai, et al.,

2013) over three-fourths of this time (Peacock, et al., 2017a; Shinkai, et al., 2009). Kick factors

considered important to impact efficiency include impact location on the foot (Asai, Carré,

Akatsuka, & Haake, 2002; Ishii, Yanagiya, Naito, Katamoto, & Maruyama, 2009; Ishii, et al.,

2012), the physical mass of the striking limb (Amos & Morag, 2002; Andersen, et al., 1999;

Moschini & Smith, 2012; Shinkai, et al., 2013), and the magnitude of ankle plantarflexion during

impact (Asami & Nolte, 1983; Kellis & Katis, 2007; Lees & Nolan, 1998; Peacock, et al., 2017a;

Sterzing, Kroiher, & Hennig, 2009).

3

The knowledge of how foot-ball impact characteristics influence impact efficiency is

limited, and conflicting results have been identified. Most notable, conflicting results exist to the

effectiveness of reducing ankle plantarflexion during impact to increase impact efficiency, a

commonly used coaching cue (Nunome, Ball, & Shinkai, 2014). While several studies have

suggested reducing ankle plantarflexion increases impact efficiency or ball velocity (Ball, Smith,

& MacMahon, 2010; Kellis & Katis, 2007; Lees & Nolan, 1998; Peacock, et al., 2017a; Sterzing,

et al., 2009), these suggestions were not supported by statistically significant results or they were

not original papers. Further, several studies have identified no associated between reduced ankle

plantarflexion and increased impact efficiency (Shinkai, et al., 2013) or ball velocity (Nunome,

et al., 2006b). Research is needed to understand how effective this coaching cue is at improving

kick performance.

Further, how players control the magnitude of ankle plantarflexion is not understood.

Increasing the stiffness of the ankle joint has been suggested as a strategy to reduce the magnitude

of ankle plantarflexion (Peacock, et al., 2017a; Sterzing, et al., 2009), and distal impact locations

on the foot have been qualitatively observed to produce larger magnitudes of ankle and foot

plantarflexion (Asami & Nolte, 1983). However, these studies each relied on qualitative

observations. Ishii, et al. (2012) identified an optimal relationship between impact location on the

foot across the proximal-distal direction with impact efficiency, and this relationship may be

associated with ankle plantarflexion. Theoretically, the resulting ankle motion will be a sum of

the internal and external torques applied to the ankle joint: an external plantarflexion torque

greater than the internal dorsiflexion torque will theoretically produce ankle plantarflexion. As

players impact distally on their foot, the external torque will be increased, causing large

magnitudes of ankle plantarflexion and possibly reducing impact efficiency. Supporting this

hypothesis, Ishii, et al. (2012) identified impact efficiency decreased with distal impact locations

distally on the foot from a location approximately 1 cm from the foot centre of mass toward the

toe. However, this must be explored. Moreover, the influence of each impact characteristic on

impact efficiency and ankle plantarflexion requires further analysis, and the effectiveness of

4

reducing the magnitude of ankle plantarflexion to improve impact efficiency, a commonly used

coaching cue (Nunome, et al., 2014), must be determined.

One issue that exists with analysing the foot-ball impact phase is the number of impact

characteristics that can influence energy transfer. The physical mass of the performer and foot

velocity just prior to impact are both known to influence impact efficiency and ball velocity

(Andersen, et al., 1999; Shinkai, et al., 2013), and the studies exploring the relationship between

reduced ankle plantarflexion and impact efficiency were performed on a group level where

differences in the physical mass and foot velocity existed (Asami & Nolte, 1983; Nunome, et al.,

2006b; Peacock, et al., 2017a; Shinkai, et al., 2013). Thus, the values observed for ball velocity

and impact efficiency likely weren’t solely due to the changes in ankle motion, but a multitude of

impact characteristics. This highlights a key issue that exists in the research of foot-ball impact:

confounding impact characteristics. Kick outcome measures are known to be influenced by

several impact characteristics, and the only way to identify the true effect of one impact

characteristic on kick outcome is when all impact characteristics other than that being analysed

are held constant. It is impossible to systematically explore the influence of individual impact

characteristics with human kickers due to the variability they produce between kicks. But, the

number of confounding characteristics can be reduced by performing an intra-individual analysis.

An intra-individual analysis removes anatomical differences and individual techniques, and task

specific strategies can also be eliminated by analysing a singular task. Or, alternatively, a

systematic exploration of individual impact characteristics can be performed by using a

mechanical kicking machine designed to replicate the impact of human kickers. Thus, exploring

the relationship between foot-ball impact with kick outcome should ensure methods that reduce

or eliminate the influence of confounding impact characteristics are used.

More research is also required to understand how foot-ball impact influences kicking

accuracy. In addition to transferring energy from foot to ball, successful kicking requires

impacting the ball to impart an appropriate combination of ball flight characteristics that enables

the ball to reach the desired target. One study has explored how foot-ball impact directly

5

influences kicking accuracy, where Hennig and colleagues identified different footwear designs

influenced a measurement of kicking accuracy (Hennig, Althoff, & Hoemme, 2009). In

subsequent articles discussing their work, the authors suggested the pressure distribution across

the anterior aspect of the foot was the primary factor influencing kicking accuracy (Hennig, 2011).

However, accurate kicking is theoretically achieved by imparting a combination of ball flight

characteristics that enables the ball to travel on an appropriate flight path that will reach the

desired target. Foot-ball impact will not directly influence kicking accuracy, rather, foot-ball

impact directly influences the ball flight characteristics. The relationship between impact

characteristics and ball flight characteristics had only been partially explored. Changes to the

medial-lateral impact location on the foot produced a trade-off between ball speed and ball spin

in soccer instep kicking (Asai, et al., 2002), an increased foot velocity translated to an increased

ball velocity (Andersen, et al., 1999), and altering the proximal-distal impact location and the

attack angle of the foot influenced ball velocity and ball spin (Ishii, et al., 2009). While both ball

velocity and spin are components of the ball flight characteristics, it is unknown how impact

characteristics influence ball flight trajectory (azimuth and elevation angles). Further, it is also

not known how ball orientation of an ellipsoidal ball, the ball used in rugby and Australian

football, influences ball flight characteristics. Research is required to determine the theoretical

link between foot-ball impact characteristics and ball flight characteristics.

The overall aim of this thesis was to explore the relationship between foot-ball impact

and kick outcome. Specifically, two areas are identified that require further analysis: the influence

of foot-ball impact characteristics on impact efficiency and ankle motion, and the influence of

foot-ball impact characteristics on ball flight characteristics and kicking accuracy. A key issue

with analysing foot-ball impact is the influence of confounding impact characteristics, and two

specific methodologies were chosen to address this issue. Firstly, a systematic exploration of

impact characteristics with a kicking machine was performed to determine the theoretical link

between individual impact characteristics (i.e. impact location, joint rigidity) and kick outcome

measures of impact efficiency, ankle plantarflexion, and ball flight characteristics. The second

6

chosen methodology was an intra-individual analysis of a submaximal accuracy task. The intra-

individual analysis of a singular task was chosen to eliminate the influence of individual

anatomical differences, individual techniques, and task specific strategies. The aim of the intra-

individual analysis was to also identify how foot-ball impact characteristics influenced impact

efficiency, ankle plantarflexion, and ball flight characteristics.

1.1. Aims

The overall aim of the thesis was to explore the relationship between foot-ball impact

characteristics and kick outcome. Two areas were identified for more research to be performed:

Aim 1: Determine how foot-ball impact characteristics influence impact efficiency

(foot-ball speed ratio, coefficient of restitution, and effective mass) and ankle

plantarflexion.

Aim 2: Determine how foot-ball impact characteristics influence ball flight

characteristics and kicking accuracy.

Each aim was answered by performing a systematic exploration of impact characteristics with a

mechanical kicking machine, followed by an intra-individual analysis of human kickers. The

specific aims of the thesis were to:

Study 1: Validate a mechanical kicking machine with a rigid ankle designed to replicate the

foot-ball impact phase of a human kicker (aim 1 and 2).

Study 2: Perform a systematic exploration of impact characteristics using a mechanical

kicking machine with a rigid ankle and an ellipsoidal ball, to determine the influence of

proximal-distal impact location, medial-lateral impact location, foot-ball angle about the x-

axis, ball flight trajectory, ball spin, ball velocity; and determine the influence of foot velocity

on ball flight trajectory, ball spin, ball velocity, and impact efficiency measures of foot-ball

speed ratio and coefficient of restitution (aim 1 and 2).

7

Study 3 and 4 both featured systematic exploration of impact characteristics using the mechanical

kicking machine to explore the influence of ankle motion on impact efficiency. Study 3 first

identified if ankle motion was influential to ball velocity and impact efficiency. Study 4 focused

on the practical implications of the finding in Study 3 by exploring different strategies players

could use to reduce ankle motion and improve kicking performance.

Study 3: Validate the ankle motion of a non-rigid ankle joint on the mechanical kicking

machine designed to replicate a human kicker, and perform a comparison of a rigid ankle

and a non-rigid ankle to determine if impact efficiency and ball velocity differ (aim 1).

Study 4: Perform a systematic exploration of impact characteristics using a mechanical

kicking machine with a non-rigid ankle to determine the influence of joint stiffness,

proximal-distal impact location and foot velocity on impact efficiency, ball velocity and

ankle plantarflexion (aim 1).

Study 5 and 6 featured an intra-individual analysis of ten players (the same player cohort)

performing the same task (30 meter drop punt kick to target). Study 5 and 6 were split as they

each answered different aims of the thesis and used a different analysis procedure. Study 5 solely

determined the influence of impact location on impact efficiency and azimuth ball flight angle.

These results were then used to discuss the philosophical question of whether a sweet spot exists

on the foot. Study 6 explored how all impact characteristics, not just impact location, influenced

kicking accuracy. Study 6 also discussed how human movement variability influenced kicking

accuracy.

Study 5: Perform an intra-individual analysis on human kickers to identify the relationship

between proximal-distal impact location on the foot and ankle plantar/dorsal flexion, foot-

ball speed ratio, coefficient of restitution, and effective mass (aim 1), and to identify the

relationship between medial-lateral impact location on the foot and azimuth ball flight

trajectory (aim 2).

8

Study 6: Perform an intra-individual analysis on human kickers to identify the relationship

between ball flight characteristics and a measurement of kicking accuracy for a submaximal

accuracy task, to identify the relationship between impact characteristics and ball flight

characteristics influential to kicking accuracy, and to identify if variability in foot-ball impact

characteristics is functional or non-functional (aim 2).

9

1.2. Thesis structure

Aim 1: Determine how foot-ball impact characteristics influence impact efficiency measures

(foot-ball speed ratio, coefficient of restitution, and effective mass) and ankle plantarflexion

Chapter 2.1: Literature review

Chapter 3: Study 1 – The impact phase of drop punt kicking: validation and experimental data of a

mechanical kicking limb

Chapter 5: Study 3 – The influence of joint rigidity on impact efficiency and ball velocity in

football kicking

Chapter 6: Study 4 – Strategies to improve impact efficiency in football kicking

Chapter 7: Study 5 – Is there a sweet spot on the foot in kicking?

Chapter 9: Study 7 – The contact area between foot and ball during impact

Chapter 10.1 (General discussion): How do foot-ball impact characteristics influence impact

efficiency and ankle plantarflexion.

Chapter 4: Study 2 – The relationship between foot-ball impact and flight characteristics in punt

kicking

10

Aim 2: Determine how foot-ball impact characteristics influence ball flight characteristics

and kicking accuracy.

Chapter 2.2: Literature review

Chapter 3: Study 1 – The impact phase of drop punt kicking: validation and experimental data of a

mechanical kicking limbChapter 3

Chapter 4: Study 2 – The relationship between foot-ball impact and flight characteristics in punt

kicking

Chapter 7: Study 5 – Is there a sweet spot on the foot in kicking?

Chapter 8: Study 6 – Kick impact characteristics of accurate football kicking

Chapter 9: Study 7 – The contact area between the foot and ball during impact

Chapter 10.2 (General discussion): How do foot-ball impact characteristics influence ball flight

characteristics and kicking accuracy

11

Chapter 2: Literature review

The two themes within this thesis are the production of ball velocity and the factors that

influence kicking accuracy. The end goal of reducing the magnitude of ankle plantarflexion

during impact is to ultimately increase final ball velocity by increasing impact efficiency. The

first section in the literature review, “The generation of ball velocity”, will discuss the previous

literature that has focused on producing ball velocity: foot velocity; the transfer of energy from

foot to ball; and impact efficiency. The second section of the literature review will cover the key

research football kicking accuracy.

2.1. The generation of ball velocity

2.1.1 Theoretical framework

The conservation of momentum combined with the coefficient of restitution indicates the

final ball velocity will be determined from the initial foot velocity and impact efficiency measures

of foot-ball speed ratio, effective mass and the coefficient of restitution. Because the foot is a non-

rigid body and comprises rotational and linear movement, the physical mass of the foot and entire

striking limb does not represent the mass component that is effective to the collision. This was

observed by Shinkai, et al. (2013) in their analysis of 51 soccer players: the physical mass of the

foot contributed approximately 84% of the effective mass used in the collision. The mass that is

effective to the collision, namely the effective mass, can be calculated from the conservation of

momentum using the initial and final foot and ball velocities, and the mass of the ball (Shinkai,

et al., 2013). Energy is lost during the collision between foot and ball due to hysteresis. Coefficient

of restitution quantifies the magnitude of elastic energy that is retained during the collision.

During foot and ball collision, both the foot, ankle and ball deform. Elastic energy is stored in this

process and is subsequently released during its reformation. The influence of foot-ball impact

characteristics can be assessed using impact efficiency measures of foot-ball speed ratio,

coefficient of restitution and effective mass as performance measures.

12

The conservation of momentum combined with the coefficient of restitution relies on the

assumption that energy is transferred solely between foot and ball during impact. In the context

of football kicking, it has been suggested that additional force is applied to the system of the foot

and ball during impact due to muscular force. Muscular force is one source of energy that has

been discussed as potentially being added during impact. Tsaousidis and Zatsiorsky (1996),

analysing the soccer toe kick, argued the conservation did not validly represent the impact of foot-

ball due to three reasons:

1. The large contact distance.

2. The magnitude of ball velocity at maximal deformation being greater than 50% of

final ball velocity.

3. The non-reduction in foot velocity during ball reformation.

Ball (2008b) also suggested muscular force could be applied during impact of drop punt kicking,

because the magnitude of change in shank angle during impact (18 ± 3°), work done on the ball

(271 ± 36 J) and contact distance (24 ± 6 cm) were also large enough for muscular force to be

applied at the hip and/ or knee joints during impact.

Muscular force also may not be applied during impact, where the increase in ball velocity

is solely due to energy/ momentum transferred from the foot to the ball. The first argument by

Tsaousidis and Zatsiorsky (1996) comprised the magnitude of distance the foot and ball travelled

together during foot-ball impact was substantial and muscular force was applied during impact.

However, it has been identified that muscular force is not applied immediately prior to impact.

Nunome, et al. (2006a) identified the quadriceps were unable to apply a concentric force during

the final 10% of leg acceleration phase prior to impact. This lack of ability to produce muscular

force was thought to be caused from the angular velocity exceeding the inherent force-velocity

relationship of the quadriceps. During phase 4 of impact (see section 2.1.2.2 for further

explanation of four impact phases), Peacock, et al. (2017a) identified foot velocity to increase 0.5

± 0.7 m/s. This increase in velocity could be due to two possibilities: the application of muscular

13

force, or, elastic energy stored in the structure of the knee and/ or ankle due to the large force

applied during impact was released. Regardless of what contributed to the increase in foot

velocity, this increase did occur during phase 4 of impact where ball velocity did not increase,

and thus this release of energy was not influential to ball velocity. The contact time (~16 ms)

observed by Tsaousidis and Zatsiorsky (1996) was also substantially larger than that observed for

drop punt, soccer instep, and rugby kicking (7 – 13 ms) (Ball, 2010; Peacock, et al., 2017a;

Shinkai, et al., 2009). Further, it has been suggested the motion of the foot and ball during impact

is passive. Nunome, et al. (2006b) suggested ankle motion was passive during impact, and the

foot-ball interaction was determined solely from the initial conditions of impact, i.e. foot speed

just prior to impact, and therefore not muscular force. Thus, while the foot and ball do travel a

distance together over a certain time, this does not mean muscular force is applied. Further, the

ability to apply muscular force may not exist until the angular velocity of the knee has decreased

partway through impact, and it is likely this does not contribute to ball velocity.

Tsaousidis and Zatsiorsky (1996) identified a non-reduction in foot velocity during ball

reformation. Subsequent studies analysing foot-ball impact have observed dissimilar results. It

has been observed in most studies that the transfer of energy from foot to ball during impact is

characterised by a reduction in foot velocity with any increase in ball velocity (Ball, Ingleton,

Peacock, & Nunome, 2013; Peacock, et al., 2017a; Shinkai, et al., 2009). These results indicate

that kinetic energy of the foot is transferred into kinetic energy of the ball, where the addition of

muscular force alone does not contribute to the kinetic energy of the ball. Shinkai, et al. (2009)

suggested the different observations (mainly about the non-reduction of foot velocity during phase

3 of impact) may have been due to different methodologies and the style of kick analysed:

Tsaousidis and Zatsiorsky (1996) analysed the soccer toe kick and measured the kinematics of

the foot and ball using a method that assumed no deformation of the foot segment and no angular

motion of the ball. Deformation of the foot and angular motion of the ball are important factors

that have been assessed in several studies (Asami & Nolte, 1983; Ishii, et al., 2009). Therefore,

the results of Tsaousidis and Zatsiorsky (1996) for the soccer toe kick appear as an anomaly to

14

what has been identified in several studies analysing foot-ball impact of drop punt and soccer

instep kicking.

Some of the evidence used by Tsaousidis and Zatsiorsky (1996) to indicate muscular

force was applied during impact have been observed in collisions where additional energy is not

added to the system. One of the key points (point 3) of the argument by Tsaousidis and Zatsiorsky

(1996) was the magnitude of ball velocity being greater than 50% than the final velocity at the

point of maximal deformation. However, other analyses of impact where no additional energy is

added to the collision have also observed this pattern (Cross, 1999), indicating this occurrence is

not specific to muscular force being applied during impact. The magnitude of final ball velocity

at the point of maximal deformation for any non-elastic collision is always greater than 50% of

final ball velocity due to hysteresis.

Tsaousidis and Zatsiorsky (1996) argued the conservation of momentum did not validly

represent the impact of football kicking due to the magnitude of muscular force applied during

impact. However, the arguments used by Tsaousidis and Zatsiorsky (1996) do not prove the

conversation of momentum combine with the coefficient of restitution does not validly represent

the impact of football kicking. There are several irregularities identified between the results of

Tsaousidis and Zatsiorsky (1996) with other analyses, where arguments 1 and 2 are do not

definitely prove the theory is not valid. Secondly, the magnitude of ball velocity at maximum ball

deformation being greater than 50% is due to hysteresis. Therefore, the addition of coefficient of

restitution to the conservation of momentum can accommodate this factor to more validly

represent foot-ball impact. Therefore, the conservation of momentum and the coefficient of

restitution can be used as a theoretical framework to analyse foot-ball impact.

15

2.1.2 Foot velocity

2.1.2.1 Contribution of foot velocity toward ball velocity

Foot velocity is an important factor toward final ball velocity, and altering foot velocity

is one mechanism that players use to control ball velocity and kick distance. The association

between higher foot velocity and higher ball velocity has been identified through multiple study

designs: regression analyses, comparisons of different performers and theoretical equations

(Andersen, et al., 1999; Ball, et al., 2010; De Witt & Hinrichs, 2012; Shinkai, et al., 2013).

Furthermore, comparisons of different kicking tasks by the same player have identified changes

in foot velocity with changes in kick distance and ball velocity (Peacock, et al., 2017a), indicating

that players can use different foot velocities for different kick distances/ tasks.

2.1.2.2 Four phases of impact

Because foot velocity prior to impact is an important factor, analysis of the interaction

between foot velocity and ball velocity is warranted. The impact phase lasts approximately 8-12

ms in duration over a distance of approximately 20-30 cm for both instep and drop punt kicking,

depending on the distance kicked (Ball, 2008a; Peacock, et al., 2017a; Shinkai, et al., 2009).

Shinkai, et al. (2009) identified four phases during foot-ball impact of the soccer instep kick,

based on the profile of foot velocity, ball velocity, and ball deformation. Using the criteria set out

by Shinkai, et al. (2009) to identify the phases during impact, Peacock, et al. (2017a) identified a

similar general pattern of foot and ball velocity in the drop punt kick; indicating the transfer of

energy from foot to ball was not influenced by the different kicking style and ball shape.

Phase 1 and 2 of impact were characterised by ball deformation. Phase 1 lasted

approximately 22% of impact duration, and was characterised by an increase in ball deformation

and reduction in foot velocity. Depending on how ball velocity was calculated, differences existed

on its motion during the phase due to the large degree of ball deformation. Shinkai, et al. (2009)

developed a method to predict the centre of gravity of the ball during impact by including ball

deformation data, and compared its velocity with that of the undeformed geometric centre of the

ball. During phase 1, the centre of gravity of the ball increased velocity immediately. The increase

16

in velocity of the geometric centre of the ball was delayed, due to deformation. Phase 2 of impact

lasted approximately 20% of impact duration, and was characterised by further increase in ball

deformation and ball velocity, and further reduction in foot velocity. The beginning of this phase

can be most easily identified from the velocity of the geometric centre of the ball. At

approximately 20% of impact duration, the beginning of phase 2, the velocity of the geometric

centre of the ball began to increase. During phases 1 and 2, velocity of the geometric centre of the

ball was less than the velocity of the centre of gravity of the ball because the centre of gravity is

moving within the geometric shell of the ball. This has implications for the calculation of further

parameters from ball velocity, such as instantaneous force for example, which could be under or

overstated if calculated from the geometric centre of the ball.

Phase 3 and 4 of impact are characterised by ball reformation. Phase 3 began at

approximately 45% of impact duration, and lasted approximately 33% of impact duration. The

onset of this phase was defined by the point of maximal deformation, coinciding with the

crossover of foot and ball velocity, where ball velocity remained higher than foot velocity for the

remainder of impact. During the phase, ball velocity continued to increase, foot velocity continued

to decrease, and the ball began reforming. Phase 4 of impact began at approximately 75% of

impact duration. Interestingly, this phase was identified by a plateau in the increase in ball velocity

and reduction in foot velocity as the ball continued to reform fully. Because ball velocity had little

increase during phase 4, a player has only three-fourths of visually identified ball contact to

effectually accelerate the ball (Shinkai, et al., 2009).

Two notable differences existed in the profile of impact for the drop punt kick compared

to the soccer instep kick. Firstly, ball velocity was non-zero at the beginning of impact for the

drop punt kick. This was due to the ball being dropped from the hand prior to being impacted by

the foot. Secondly, foot velocity increased by 0.5 m/s in phase 4. Peacock, et al. (2017a) identified

two factors that may explain this increase in foot velocity: muscular force may have been applied

during foot-ball impact, where it was not until phase 4 where ball velocity plateaued that the

17

increase in foot velocity appeared; or, elastic energy stored in the soft-tissue structures

surrounding the foot and/ or knee was released, thus increasing the linear velocity of the foot.

2.1.2.3 An alternate profile of impact

During foot-ball impact of the less popular soccer toe-kick, Tsaousidis and Zatsiorsky

(1996) identified three phases, rather than four. During deformation, phases 1 and 2 were similar

to those identified by Shinkai, et al. (2009) and Peacock, et al. (2017a). Ball reformation, however,

was not split into two phases but was treated as one phase (phase 3). Interestingly, there was no

reduction in foot velocity during this phase, but it can be identified approximately midway

through that ball velocity began to plateau. Shinkai, et al. (2009) noted this discrepancy may have

been due to two factors: firstly, the particular point of the foot to calculate velocity was not

identified; and secondly, Tsaousidis and Zatsiorsky (1996) assumed no deformation of the toe

part of the foot that penetrated into the ball.

2.1.2.4 Ball deformation and reformation

The point of maximum deformation occurs at the crossover point of foot and ball velocity

(Shinkai, et al., 2009). The timing of these events is logical; when the foot is in contact with the

ball but is travelling faster, the ball must be deforming. When ball velocity is greater than foot

velocity, the ball is travelling away from the foot, and thus the ball must be reforming. Shinkai,

et al. (2009) reported a maximum deformation of 6.2 ± 0.6 cm for instep kicking, Ishii, et al.

(2012) reported maximum ball deformation was between the range of 2.9 to 6.5 cm.

2.1.2.5 Force applied between foot and ball

Quantifying the magnitude of peak force between foot and ball can improve our

understanding of injury risk associated with excessive football kicking: anterior ankle

impingement syndrome. Tol, Slim, van Soest, and van Dijk (2002) tested two hypotheses that

were developed to explain the occurrence of anterior ankle impingement syndrome: (i) hyper-

ankle plantarflexion; (ii) the magnitude and location of force applied to the ankle joint. By

analysing 150 kicks from 15 elite soccer players, the authors identified hyper-ankle plantarflexion

18

occurred only in the minority of kicks, therefore the magnitude and location of force applied to

the foot and ankle was likely the main cause of the condition.

Measuring the average force applied to the ball can easily be obtained by the change in

ball velocity, contact time and ball mass (Peacock, et al., 2017a; Shinkai, et al., 2009; Tol, et al.,

2002). Average force differs between kick distances (Ball, 2008b; Peacock, et al., 2017a),

whereby the increased foot velocity was the considered cause of greater average force (Peacock,

et al., 2017a). Greater average force has also been identified in senior compared to junior players

(Ball, et al., 2010), and between the preferred compared to the non-preferred limb (Smith, Ball,

& MacMahon, 2009) (calculated post-hoc by the author of the present thesis).

Several authors have identified the maximum force applied between foot and ball.

Shinkai, et al. (2009) reported a maximum deformation of 6.2 ± 0.6 cm for instep kicking, and at

this event calculated a peak force of 2926 ± 509 N. Ishii, et al. (2012) developed a method to

calculate instantaneous force during foot-ball impact from ball deformation, but did not report

peak values. Tol, et al. (2002) estimated peak force during impact by multiplying average force

(calculated from the change in ball velocity, contact time and ball mass) by π/2, assuming the

force profile followed a half sine-wave. Shinkai, et al. (2009) identified this method severely

underestimated the true magnitude of peak force applied during impact: Tol, et al. (2002)

estimated peak force to be 1610 N, approximately 1.6 times the average force of 1025 N; whereas

Shinkai, et al. (2009) measured a peak force of 2926 N, approximately 2.1 times the average force

of 1403 N. As Shinkai, et al. (2009) identified the method by Tol, et al. (2002) underestimated

their measured magnitude of peak force, Iga, Nunome, Sano, Sato, and Ikegami (2017) set to

explore the validity of measuring impact force using the various methods in the literature using a

force plate as a criterion for validation. They developed a new method to measure force, citing

increased accuracy compared to the previous methods, and future work is looking to utilise this

method in football kicking actions.

19

2.1.3 Impact efficiency

Impacting the ball efficiently, whereby the maximum ball velocity is attained for a given

foot velocity, is desirable for players. As identified from the energy transfer principles, impact

efficiency, as measured from foot-ball speed ratio, will be determined by the effective mass of

the striking limb and the coefficient of restitution for the collision. Several foot-ball impact

characteristics have been identified to influence impact efficiency (foot-ball speed ratio), effective

mass and coefficient of restitution.

2.1.3.1 Impact location

Moving impact location distally on the foot will theoretically increase ball velocity

linearly. Andersen, et al. (1999) rearranged an equation combining the conservation of angular

momentum, conservation of momentum, and coefficient of restitution to predict ball velocity, and

found it to be in good agreement with their experimental data. From this equation, an increase in

the distance between the knee and impact location on the foot/ ball centre will increase ball

velocity. Ball velocity increases because distance between the rotating knee and the impact

location increases with a distal impact location, thus translating to a higher velocity of the

impacting point.

An alternative theoretical relationship identifies an optimal relationship exists between

proximal-distal impact location with ball velocity. Analysing side and instep kicking techniques,

Ishii, et al. (2009) and Ishii, et al. (2012) identified an optimal impact location for each kick within

their theoretical equations based upon the impact dynamic theory. This equation predicts ball

velocity was maximum with an impact location approximately 1 cm toward the toe for instep

kicking, and approximately 3.5 cm toward the heel for the side kick. Validation of their models

identified good agreement with the experimental data: absolute differences existed with

experimental data and the model, however, the relationships between impact location with ball

velocity were consistent. To facilitate changes in impact location for the instep kick, they altered

the height of the ball above the ground by using a cardboard tee. Although this might violate

20

ecological validity, this constraint yielded a produced a large range of impact locations (0.16 m)

across the dorsal aspect of the foot.

A finite element analysis identified changes to impact location in the medial-lateral

direction from the foot centre of mass decreases ball velocity, but increases ball spin. Asai, et al.

(2002) compared the offset distance, calculated from the distance between foot-ball impact and

the centre of the ball, and identified ball velocity was maximal with an offset distance of 0 cm,

where the impact location passed through the centre of the ball. There was a trade-off between

ball velocity and spin rate. Ball velocity decreased when the offset distance increased in either

direction (positive or negative), while the spin rate increased.

2.1.3.2 Physical mass

Increasing the physical mass of the shoe, such as by adding masses to the foot, increases

the effective mass of the foot. This might appear to be an effective strategy to increase ball

velocity, given Nunome, et al. (2006a) identified players were unable to apply force through the

quadriceps just prior to impact as the knee extension velocity was too great for the muscles to

contract. The results of Nunome, et al. (2006a) identify the increase in knee extension velocity

was limited by the capability muscle contractile velocity, thereby increasing the mass would mean

a lower velocity is required for the constant momentum. However, Amos and Morag (2002) and

Moschini and Smith (2012) both identified increasing the physical mass resulted in no change to

final ball velocity, as the momentum of the limb remained constant as the effective mass increased

but foot velocity decreased. This does indicate, however, that because ball velocity was constant

but foot velocity reduced, that increases to effective mass will increase foot-ball speed ratio.

A greater physical mass of the performer translates to a greater foot-ball speed ratio.

Shinkai, et al. (2013) identified in a cross-sectional analysis of 51 junior to senior players that ball

velocity increased with player age. Two factors caused the increased ball velocity: higher foot

velocities and higher physical masses. This indicates that despite higher leg masses they also

increased foot velocity, likely due to greater strength levels. Interestingly, the physical mass of

21

the players also correlated with impact efficiency measures. The sum of the shoe and foot mass

corresponded to 84.0 ± 9.6% of their effective mass. Further, effective mass correlated positively

with foot-ball speed ratio (r = 0.89). This indicates increases to effective mass, through physical

mass, will increase foot-ball speed ratio.

2.1.3.3 Reducing the magnitude of foot and ankle plantarflexion during impact

During foot-ball impact, the ankle joint is forced into passive plantarflexion (Nunome, et

al., 2014; Nunome, et al., 2006b; Peacock, 2013; Peacock, et al., 2017a; Shinkai, et al., 2009;

Shinkai, et al., 2013). Analysis within the foot-ball impact phase identified three general patterns

of ankle motion to exist within both drop punt and instep kicking (Peacock, 2013; Shinkai, et al.,

2009): (1) distinct plantarflexion through the entire duration of impact; (2) initial dorsiflexion for

the first fourth-to-third of impact duration, followed by distinct plantarflexion; (3) dorsiflexion

through the entire duration of impact. Both Shinkai, et al. (2009) and Peacock (2013) identified

most players produced pattern number two, and only one player who produced a unique technique

displayed pattern three.

The foot metatarsophalangeal and ankle joint motion have been identified as an important

factor toward producing ball velocity (Asami & Nolte, 1983; Ball, et al., 2010; Peacock, 2013;

Peacock, et al., 2017a; Plagenhoef, 1971; Sterzing, et al., 2009). Asami and Nolte (1983) first

identified a relationship between foot and ankle plantarflexion with ball velocity. In an analysis

of six players, including one international player, 19 kicks were analysed and correlations were

identified for ankle plantarflexion (r = -0.409;) and foot plantarflexion (r = -0.805). Post-hoc

analysis by the author of this thesis identified the correlation between ankle plantarflexion with

ball velocity was p = 0.08, and the correlation between foot plantarflexion with ball velocity was

p < 0.001. These results first introduced the concept that increasing rigidity, to reduce the

magnitude of foot and ankle plantarflexion, was beneficial to ball velocity. Qualitative analysis

by Asami and Nolte (1983) identified impacting distally on the metatarsus and/ or phalanges

produced the large foot plantarflexion. Shinkai, et al. (2013) performed a cross-sectional analysis

on the impact characteristics of 51 junior to senior players. Despite identifying a non-significant

22

correlation between change in ankle plantarflexion with foot-ball speed ratio (r = -0.36), post-hoc

partial correlation analysis by the author of this thesis identified a significant relationship, partial

to effective mass (r = -0.79; p < 0.0001). This partial correlation is warranted, because the physical

mass of the performer is known to increase foot-ball speed ratio (Amos & Morag, 2002).

Therefore, strategies to reduce foot and ankle motion during impact appear to be beneficial to

final ball velocity.

Relying on anatomical structures at the end of the ankle and foot plantarflexion range of

motion increases their rigidity. This strategy is considered effective at improving impact

efficiency due to a reduced ankle plantarflexion during impact. Sterzing, et al. (2009) compared

maximal ball velocity kicking between several shoe types, barefoot and with a sock, and stated

“kicking barefoot provided superior collision biomechanics”, due to a greater magnitude of ankle

and foot plantarflexion adopted at the beginning of impact. Peacock, et al. (2017a) identified,

despite a greater force applied to the foot, that maximal kicks produced significantly less ankle

plantarflexion during impact because they adopted a more plantarflexed position at the beginning

of impact. As the foot and ankle are forced into plantarflexion during foot-ball impact, the

stiffness within the foot and ankle joint increases as the soft tissue structures are stretched and the

hard tissue structures come in direct contact.

A players strength may also improve a player’s ability to maintain ankle and foot position

during impact. Ball, et al. (2010) compared the impact characteristics of senior to junior

Australian football players. Despite a larger force applied to the foot for the senior players, they

produced a significantly smaller magnitude of change in ankle plantarflexion during impact. Due

to the higher levels of strength within the senior players, the authors suggested increasing

muscular strength may be an effective strategy to increase rigidity in the foot and ankle segment,

but did throw caution to this mechanism as other impact characteristics such as foot-ball

orientation may have also caused this difference. Further, senior players are also likely to have

greater body mass, also increasing foot-ball speed ratio in the senior players.

23

The conservation of momentum combined with the coefficient of restitution can provide

two mechanisms to explain how energy transfer between foot and ball might be influenced by

ankle and foot motion during impact (Equation 2.1): effective mass and coefficient of restitution.

In their literature review, Lees and Nolan (1998) introduced the conservation of momentum

theory combined with the coefficient of restitution to describe the impact between foot and ball.

They stated the effective mass is the mass equivalent of the striking object (foot and shank) that

is made more rigid from muscle activation, and the coefficient of restitution relates to the firmness

of the foot due to foot plantarflexion. In another review of the literature, Kellis and Katis (2007)

state less deformation in the foot translates to higher coefficient of restitution. Similarly, Sterzing,

et al. (2009) stated greater change in ankle plantarflexion during impact resulted in more energy

dissipation, which can be interpreted as reduces to the coefficient of restitution. These three

studies, despite using several different terms, have used the concepts of energy transfer to describe

how reduced ankle and foot motion influences ball velocity: effective mass and coefficient of

restitution. The effective mass, as introduced by Kellis and Katis (2007) and Lees and Nolan

(1998), appears to be influenced by change in ankle plantarflexion during impact. Whereas

coefficient of restitution is influenced by change in foot plantarflexion during impact (Kellis &

Katis, 2007; Lees & Nolan, 1998) and change in ankle plantarflexion (Sterzing, et al., 2009).

𝑣𝑏 = (

1 + 𝑒

1 + 𝑚𝑏 𝑚𝑓⁄) ∙ 𝑢𝑓 + (





Several other studies have identified differences in coefficient of restitution between

kicking groups, identifying the mechanical properties and the motion of the foot and ankle during

impact are influential to final ball velocity. Andersen and colleagues have identified several

circumstances where coefficient of restitution has differed (Andersen, et al., 1999; Andersen,

Kristensen, & Sorensen, 2005, 2008; Dørge, et al., 2002). In their first study (Andersen, et al.,

1999), they identified coefficient of restitution varied within a group of athletes, whereby the

24

mechanical properties of the shoe, foot and ankle joint were suggested to probably contribute to

the differing values. A comparison of preferred and non-preferred kicking limbs identified

coefficient of restitution differed, and stated a small difference in the extension and stiffness of

the foot and ankle may alter the coefficient of restitution (Dørge, et al., 2002). They also

performed a series of studies comparing the toe and instep style of kicks (Andersen, et al., 2005,

2008). The key difference between the toe and instep kicks is the impact location on the foot: the

toe kick impacts the ball with a notably smaller contact area compared to the instep kick. To

determine the differences in kicking dynamics between the two techniques, they first performed

a systematic comparison with a pendulum with two impacting surfaces of different areas: a

smaller contact area to represent the toe kick; and a larger contact area to represent the instep kick.

The results identified a smaller contact area produced higher coefficient of restitution values,

suggesting the toe kick would produce an improved ball velocity. However, subsequent

comparisons between the toe and instep kick styles with human players identified this

performance advantage reduced at moderate-high foot velocities (> 15 m/s), where they

speculated the stiffness in the foot and ankle diminished. This suggests that foot and ankle motion

again may be detrimental to kicking performance.

The effectiveness of reducing the magnitude of ankle and foot plantarflexion during

impact is not fully understood. The literature presented thus far indicates there is a positive

relationship between foot and ankle motion during impact with a sound theory describing the

interaction. However, several studies have also identified non-significant and conflicting results

in the relationship between change in ankle plantarflexion with ball velocity. Nunome, et al.

(2006b) identified an athlete that produced a relatively high ball velocity also demonstrated

substantial change in ankle plantarflexion during impact in respect to the analysed group. Despite

identifying a significant difference in ankle plantarflexion during impact between two tasks,

Peacock, et al. (2017a) identified no significant difference in foot-ball speed ratio. Shinkai, et al.

(2013) identified a non-significant relationship between change in ankle angle with foot-ball

speed ratio in a group of 51 players. While subsequent post-hoc partial correlations with effective

25

mass by the author of the present thesis suggests this relationship is significant, effective mass

might also be dependent on ankle motion (Lees & Nolan, 1998), thus this result should be taken

with caution. Despite identifying a significant difference in change in ankle plantarflexion during

impact, Ball, et al. (2010) identified a non-significant difference (p = 0.02; d = 0.7) in foot-ball

speed ratio. While the p-value was less than 0.05, this was non-significant due to Bonferroni

adjustment. Further, given foot-ball speed ratio is influenced by the physical mass of a performer,

this observed difference might also be due to the physical mass changing between the senior and

junior players, not ankle motion.

To further confuse the influence of foot and ankle motion on impact efficiency during

impact, the previous studies that promoted a clear relationship between foot and ankle motion

with ball velocity each have their limitations. In fact, the only result that provides a statistically

significant relationship between ankle motion with foot-ball speed ratio is the post-hoc partial

correlation of Shinkai, et al. (2013) performed by the author of this thesis, which should be taken

with caution. Lees and Nolan (1998) and Kellis and Katis (2007) introduced the concepts of

effective mass and coefficient of restitution, and how each are influenced by ankle and foot motion

during impact. However, these claims were not based on any data as they were not original papers.

Despite Sterzing, et al. (2009) discussing the magnitude of foot and ankle plantarflexion at the

beginning of and during impact in their comparison of barefoot to shod kicking, they did not

quantitatively measure foot and ankle motion. Rather, they performed a qualitative analysis on

one individual within the group, and inferred that this result was consistent for all players within

the group. Furthermore, the statistical results do not support their claims that ball velocity was

higher in the barefoot over shod conditions, which is the foundation of their link between foot and

ankle motion with ball velocity. The authors performed an ANOVA analysis between the groups:

however, firstly, the ANOVA at the group level was non-significant (p = 0.05); and secondly,

they did not perform any post-hoc analyses to identify direct differences between the barefoot

with any shod conditions. Rather, they stated “there was a strong trend toward higher ball velocity

in the barefoot condition”. While Asami and Nolte (1983) did identify a significant relationship

26

between foot plantarflexion with ball velocity, foot velocity was also identified as a key

determinant of ball velocity (r = 0.738), where the analysis of ankle and foot motion must be made

with impact efficient measure of foot-ball speed ratio, or energy transfer mechanisms of

coefficient of restitution and effective mass. It is possible foot velocity caused the greater final

ball velocity and greater change in plantarflexion during impact. Thus, there is no empirical

evidence supporting the relationship between foot and ankle motion with impact efficiency,

possibly explaining why several researchers have identified dissimilar results (Nunome, et al.,

2006b).

2.1.4 Summary of factors influential to ball velocity

Currently, the only strategy that players can use to increase ball velocity that has statistical

and theoretical support is through an increased foot velocity. However, the type of the relationship

(i.e. linear, non-linear) is not yet fully understood, and this has implications for future analyses.

Although Peacock, et al. (2017a) identified foot-ball speed ratio was non-significant between the

two kicking tasks, they argued that the greater foot velocity in the maximal distance kick

confounded the results, where reducing reduced ankle plantarflexion was beneficial to foot-ball

speed ratio. They argued that foot-ball speed ratio would decrease with an increasing foot

velocity, assuming all other characteristics were held equal. This suggests the relationship

between foot velocity with ball velocity was non-linear, rather, the increase in ball velocity

diminished with increases in foot velocity. This has implications for future comparisons. If impact

efficiency measures are dependent on foot speed, then comparisons of different conditions, such

as different footwear designs, must take this information into consideration to understand where

differences might exist.

No study has identified the relationship between impact location with ball velocity under

kicking conditions. The studies that have analysed the relationship between impact location with

ball velocity have used theoretical equations (Andersen, et al., 1999; Asai, et al., 2002; Ishii, et

al., 2009, 2012). Further, conflicting relationships exist within the validated models that predict

ball velocity from impact location. Due to difficulties with measuring impact location between

27

the foot and ball, no study has explored this relationship using experiment data. Therefore, a

methodology must be developed to calculate impact location in three-dimensional space to further

understand if and why impact location influences ball velocity.

Lastly, it is widely established in the scientific literature that reducing change in

plantarflexion of the foot and ankle during impact will translate to an increased ball velocity.

However, critical analysis of the literature identified there is no empirical evidence supporting

this theory (Asami & Nolte, 1983; Peacock, et al., 2017a; Sterzing, et al., 2009), or, several

authors have introduced the concepts in literature reviews without evidence supporting their

claims (Kellis & Katis, 2007; Lees & Nolan, 1998). Further, several studies have identified no

relationship between reducing change in ankle plantarflexion with increased ball velocity, stating

the relationship requires an appropriate analysis (Nunome, et al., 2006b; Shinkai, et al., 2013).

More research is required to understand if and why ankle and/ or foot motion is influential to

impact efficiency and/ or ball velocity, where the influence of confounding impact characteristics

is either eliminated or controlled for.

2.2. Kicking accuracy

2.2.1 Theoretical framework

2.2.1.1 Measurements of kicking accuracy

In gameplay, a successful shot at goal occurs when the ball successfully passes through

the space bounded by the goal posts. When passing, a kick can be classified as successful if the

desired team member receives the ball. There are levels of success for passing, whereby passing

to a team member without deviating from a specific path on the field enabling them to continue

attacking or move into an attacking position can be considered the ultimate form of success.

However, there are times when a pass will still be successful despite this occurring: a fellow team

member can deviate from their specific path on the field and receive the ball; or, if the pass is not

received by the desired target but is received by a different team member. For all conditions,

though, a player will select a specific target whereby the success of this outcome is dictated by

28

the distance the ball travels from this target in relation to the context of the game. Thus, there are

levels of accuracy that differentiate the outcome of the kick to be successful or unsuccessful, such

as travelling within the goal posts when scoring or within reach of a fellow team member when

passing.

The measurement of kicking accuracy can be reduced to a two-dimensional coordinate

within the vertical and horizontal planes perpendicular to the direction of the kick. In the vertical

plane, the accuracy outcome of a kick can be reduced to a two-dimensional coordinate comprising

the horizontal and vertical distances from the target. In the horizontal plane, the accuracy outcome

can also be reduced to a two-dimensional coordinate comprising the perpendicular and parallel

distances. Depending on the desired outcome of the kick, either of the planes are a more suitable

measurement plane. When scoring and passing, the vertical plane is often most representative

given the orientation of both players and goals on the field (Figure 2.1).

Figure 2.1: Measurements of kicking accuracy as a two-dimensional coordinate in the

vertical plane when scoring (A) and passing (B) in different codes of football. The

direction of the coordinates is represented by the red arrows.

Other studies assessing football kicking accuracy and sports that demand high end-point

accuracy have taken other approaches to measuring kicking accuracy and/ or identify factors

associated with accuracy. Rather than splitting the end-point position into a two-dimensional

coordinate, the resultant distance from the desired target can be measured (Hennig, et al., 2009).

29

This can reduce complexity of the subsequent analysis because only one performance outcome is

determined. But, the ability to identify direct mechanisms is often reduced because of the scalar

nature of measurement. For example, two kicks that miss the target by both 1 m on the left and 1

m on the right will travel on distinctly different flight paths despite both displaying an accuracy

measurement of 1 m. Defining boundaries of successful and unsuccessful outcomes have also

been employed (Atack, Trewartha, & Bezodis, 2017; Dichiera, et al., 2006; Phillips, Portus,

Davids, & Renshaw, 2012), enabling the option of group analysis to be performed. This

measurement does have a real-world context because the outcome of kicking often comes down

to the ball passing within a boundary, such as the goal posts. However, this method again limits

the opportunity for mechanisms to be identified because continuous measures are not employed.

Further, kicks that may be characterised by a small difference in the real world may be classed as

different outcomes. For example, two kicks that pass immediately either side of the goal posts,

while only differentiating by a small distance such as 10 cm, will be classed as different outcomes.

To reach a specific target, the ball must travel on a necessary flight path once the ball

leaves contact with the foot. During this flight path, the ball is in projectile motion and there is

nothing a player can do to alter its path. In addition to gravity, aerodynamic forces (including drag

force, lift force and buoyancy) are applied to the ball (Goff, 2013). Because there are several

forces applied to the ball, there are multiple combinations of flight characteristics that will enable

a specific target to be reached. For example, a lower elevation angle but higher ball velocity can

reach the same target. Mechanically, to kick toward a specific target, a player will impart a

combination of ball flight characteristics by impacting the ball with their foot. Thus, to identify

how foot-ball impact influences kicking accuracy, taking the approach of foot-ball impact – ball

flight characteristics – kicking accuracy measurement will enable the direct mechanisms to be

outlined. This was the theoretical framework chosen for this thesis to determine how kicking

accuracy is influenced by foot-ball impact characteristics.

30

2.2.2 The ball flight path

Ball flight characteristics can be defined by the magnitude of ball velocity (m/s), azimuth

and elevation trajectories, ball orientation in the X, Y and Z axes, and ball angular velocity (spin)

in the X, Y and Z axes (Figure 2.2).

Figure 2.2: Ball flight characteristics

Gravity and aerodynamic forces of drag and lift are applied to the ball as it travels through

air as a projectile (Goff, 2013). Carré, Asai, Akatsuka, and Haake (2002) performed a systematic

exploration of ball flight spin characteristics to calculate the drag and lift coefficients for the

spherical soccer ball, where it was identified a back-spin will produce a positive lift force onto

the ball and greater velocity increases the drag force. For non-spherical balls, such as the

ellipsoidal rugby league and Australian football balls, the orientation of the ball also influences

the aerodynamic forces on the ball (Alam, Subic, Watkins, & Smits, 2009). No work has been

performed on a spinning ellipsoidal shaped football, thus we can only speculate, based on the

results of Alam, et al. (2009) and Carré, et al. (2002), that an ellipsoidal ball slightly tilted with

θ° = Azimuth trajectory

θ° = Elevation trajectory

x

y

z

31

back-spin will produce a lift force pushing the ball off plane. This is likely why players perform

the drop punt kick most frequently in Australian football; the back-spin imparted onto the ball

produces a stable flight path.

Several studies have developed mathematical models to predict the flight path and

outcome of football kicks. Atack, Trewartha, and Bezodis (2015) developed a mathematical

model to determine the success of rugby union place kicking toward goal from 22.0 m. This model

included initial ball flight characteristics from eight trials, ball mass, ball size and spin coefficients

from a previous study (Djamovski, Rosette, Chowdhury, Alam, & Steiner, 2012). Carré, et al.

(2002) more extensively developed a mathematical model predicting the flight path of the

spherical soccer ball. A cannon fired the ball at various velocities and spin rates, where two

cameras captured the initial velocity, elevation angle and the flight path over 10 meters. The

values of coefficient of drag and lift were calculated for each trial, and mathematical modelling

was applied to determine the relationship between ball angular velocity with coefficient of lift,

and ball linear velocity with coefficient of drag.

2.2.2.1 Optimising ball flight characteristics to increase the likelihood of successful kicking

Following on from developing the relationships between flight characteristics with

aerodynamic forces, Carré, et al. (2002) explored the predicament players face when performing

a free-kick at goal. Under the hypothetical situation of taking a free-kick 18 m from goal with a

ball velocity of 25 m/s, the shortest time period of 0.9 s for the ball to reach the top corner of the

goal is with no spin imparted onto the ball. A player might instead choose to impart a spin onto

the ball, which would result in a reduction in ball linear velocity (due to a trade-off between ball

linear velocity and ball angular velocity). With adjusting the flight characteristics to ensure the

ball will reach the target, the flight time would increase to 1.6 s. It might seem obvious to perform

Kick A with no ball spin because the shortest flight time will ensue, where the goal keeper would

need to react and intercept the ball with the least time period. However, applying the ball curve

might give the impression to the goal keeper that the ball will miss the goal, thus they may delay

32

their attempt or choose not to make an attempt at intercepting the ball. The authors noted that an

experienced player would be able to impart a high ball linear and angular velocities.

Peacock, et al. (2017a) identified elite players altered the ball flight characteristics in a

comparison of a maximal distance kick to an accuracy based task. For the accuracy based task,

the players kicked toward a sports training mannequin 20m away. Comparatively, the ball

travelled approximately 60 m in the maximal distance task. Rather than reducing ball velocity

from 28.1 m/s in the maximal distance kick to one-third to merely reach the required distance,

players reduced ball velocity by 21% down to 22.1 m/s and lowered elevation flight trajectory

from 30° to 15° to ensure the ball would intercept the target. This change in ball flight

characteristics, a lower elevation angle but increased ball velocity, was discussed to benefit the

chance of success for the task: the relative target area is increased with a lower ball flight

trajectory. Because the target was aligned vertically, the relative target area (the perpendicular

distance of the target relative to the ball flight trajectory) is increased with a lower elevation angle.

This process is similarly discussed in basketball shooting, whereby an increased elevation

increases the relative area of the horizontal hoop. Additionally, a lower elevation angle and higher

ball velocity will travel a constant distance but in a shorter time period. Given the players were

elite, ensuring the ball is received by team members when passing in the shortest time period is a

strong demand within gameplay because a longer flight time can increase the opportunity for

opposition players to intercept the ball. This strategy may be engrained in their ability to kick

toward targets.

2.2.3 The relationship between foot-ball impact characteristics with ball flight

characteristics

Understanding how players impart the combination of ball flight characteristics onto the

ball is important to develop coaching cues for accurate kicking. In the first of the two-paper series

investigating the trade-off between ball velocity and ball spin, Asai, et al. (2002) identified players

can alter the magnitude of ball velocity and ball spin by changing the medial-lateral impact

location between the foot and ball. Thus, foot and ball impact location influences ball spin and

33

ball velocity. An impact location through the centre of the ball imparts a maximum ball velocity

with no ball spin, and ball velocity decreases and ball spin increases as impact location is moved

either direction from the centre. Thus, an optimal relationship exists between impact location with

ball velocity, and an inversed optimal relationship exists with ball spin. Peacock (2013), which is

the original thesis that Peacock, et al. (2017a) was developed from, discussed possible

mechanisms of how the players imparted the differing ball flight characteristics between the

maximal distance kick and 20 m accuracy task. Ball flight trajectory reduced from 30° in the

maximal distance kick to 15° in the 20 m accuracy task. Foot angle, as measured in the global

coordinate system, was aligned closer to the vertical by 15° in the accuracy task, and the change

in ankle plantarflexion during impact was greater in the accuracy task, both were factors suggested

to translate to the differing elevation ball flight trajectory.

Ishii and colleagues developed two mathematical models to predict ball velocity and ball

spin for the soccer instep kick and soccer sidestep kick (Ishii, et al., 2009, 2012). For the soccer

instep kick, impact location across the proximal-distal direction of the foot was treated as the

independent variable, where ball velocity, standardised to foot velocity (foot-ball speed ratio),

followed an optimal relationship with a maximum velocity at approximately 1 cm from their

defined foot centre of mass in the proximal direction. For the soccer sidestep kick, attack angle

(comprising foot trajectory and foot angle) and impact location across the proximal-distal

direction on the medial surface of the foot were treated as the independent variables. Foot-ball

speed ratio was identified to be maximum with an impact location 5 cm to the heel from the foot

centre of mass with an attack angle of approximately 10 degrees. Ball spin was maximum with

the opposite combination of impact characteristics: an impact location approximately 7 cm from

the foot centre of mass in the distal direction with an attack angle of 30 degrees. Both of these

models were developed based upon the impact dynamic theory, comprising the angular and linear

impulse-momentum relationship and coefficient of restitution, and were validated using

experimental data from players.

34

2.2.4 Other factors influencing kicking accuracy

By measuring kicking accuracy and treating it as a dependent variable, several more

factors have been identified to be associated with kicking accuracy: kinematic and kinetic patterns

during the forward leg swing, and footwear designs. Both the kinematic and kinetic patterns and

footwear designs are important factors for the execution of the kicking skill, thus it is warranted

to identify how they influence kicking accuracy. However, by analysing the direct relationship

between kinematic and kinetic patterns and footwear designs with kicking accuracy, key

information, such as ball flight characteristics and impact characteristics, can be missed, possibly

confounding the influence of several factors identified through this project design. Further, the

direct mechanisms influencing kicking accuracy cannot be identified, rather, only associations are

generated. Regardless, important information about factors influencing kicking accuracy can be

identified.

2.2.4.1 Kinematic and kinetic patterns

Two studies have identified how kinematic and kinetic patterns are associated with

kicking accuracy by comparing less accurate to more accurate kickers (Atack, et al., 2017;

Dichiera, et al., 2006). Atack, et al. (2017) identified rugby place kickers who executed a kick

that travelled less than 32 m and to the left of the goals relied more on the tension arc – the relative

pelvis-thorax rotation – compared to those that travelled over 32 m in distance, suggesting reliance

on this tension arc may be associated with reduced accuracy. Dichiera, et al. (2006) split 10 elite

players performing the drop punt kick into accurate (N = 5) or inaccurate (N = 5) kicking groups

based on the performance of 20 kicks, and subsequently compared sagittal plane kinematics. Hip

flexion of both support and striking limbs, greater knee flexion in the support limb, and anterior

pelvic tilt differed between the groups at certain events during the execution of the skill. The key

finding of this study was in the support limb: they identified lowering the body centre of mass,

by greater knee flexion in the support limb, may be associated with improved kicking accuracy

by increasing the stability of the player.

35

2.2.4.2 Footwear designs

Footwear designs that promote a more homogenous surface between the foot and ball to

reduce pressure peaks have been stated to be the primary factor of accurate kicking (Hennig, 2011,

2014; Hennig & Althoff, 2018; Hennig & Sterzing, 2010). The accuracy of kicking with five

different footwear designs and with barefoot to a target 10m in distance was compared, where it

was identified that kicking barefoot produced the least accurate outcome (Hennig, et al., 2009).

The authors stated subsequent testing with a pressure sensor attached to the impact area across

the dorsal aspect of the foot identified reduced peak pressures in the shoe that yielded higher

accuracy, whereby they suggested large pressure gradients across the foot-ball surface caused by

anatomical structures (bony prominences) could be the reason explaining these results. To further

test this theory, the authors stated that adding padding between the length of the first metatarsal

and the longitudinal arch and between the gaps of the phalanges further reduced the pressure

peaks across the foot and improved accuracy.

Hennig, et al. (2009), however, did not report the results or statistics to support their claim

that pressure differed between the two accurate and less accurate footwear designs, nor any results

or statistics on the pressure differences and kicking accuracy between the padding and non-

padding conditions. Over several review papers and book chapters discussing their work (Hennig,

2011, 2014; Hennig & Althoff, 2013, 2018; Hennig & Sterzing, 2010), the authors released

fragments of the results from the initial study (Hennig, et al., 2009) to support these additional

claims – the difference in peak pressure gradients between the shoes producing more and less

accuracy (Hennig, 2011; Hennig & Althoff, 2018) and the differences in accuracy incurred from

added padding onto the shoe (Hennig & Althoff, 2018). However, the results do not clearly

identify accuracy was improved from a more homogenous pressure distribution between the foot

and ball.

Between the accurate and less accurate footwear designs, it was stated the pressure for

the accurate footwear was more homogenously distributed (Hennig, et al., 2009). In the

subsequent studies, it was stated the location of the centre of pressure differed to be medial and

36

proximal in the more accurate footwear design, and the pressure differences between adjacent

transducers was just under 20% more in the less accurate shoe (Hennig, 2011; Hennig & Althoff,

2018). However, standard deviation was not presented, nor was a statistical analysis performed.

Thus, the generalisability of this result between individuals that would exhibit differing kicking

techniques and foot shapes is somewhat limited.

The effectiveness of additional padding to improve accuracy may also not be as effective

as originally stated, because the influence of padding produced a non-significant influence on

kicking accuracy. It was stated in the original study that adding padding reduced the high-pressure

differences gradients across the foot improved shooting accuracy. However, the influence of

padding in comparison to the non-padding kicking conditions, as released in a subsequent book

chapter (Hennig & Althoff, 2018), produced non-significant difference in kicking accuracy (p =

0.11) and non-significant difference in kicking precision (p = 0.12). No mean and standard

deviations for kicking accuracy nor kicking precision were reported, rather, the authors stated

there was a trend toward improved performance when kicking with padding (Hennig & Althoff,

2018). Again, the non-significant result questions the generalisability to a greater population and

the overall effectiveness of the intervention.

From these results, and despite not testing any other mechanism, the authors state the

homogeneity of pressure between the shoe upper and the ball is the primary factor that influences

kicking accuracy (Hennig, 2011, 2014; Hennig & Althoff, 2018; Hennig & Sterzing, 2010). The

design of the footwear to reduce the lower the pressure differences across the dorsal aspect of the

foot does appear to influence accuracy, however, this theory does not explain some important

instances of kicking accuracy: why players produce a percentage breakdown of accurate and

inaccurate kicks within the one task. When performing repetitions of a singular task, and

depending on the complexity of the task, even elite players produce an undesired percentage

breakdown of accurate and inaccurate kicks. This is evident in the literature of football kicking:

Dichiera, et al. (2006) identified out of ten elite Australian football players the highest percentage

of accuracy attained was 75% and the lowest at 20%. The complexity of the task will influence

37

the percentage breakdown – but, it is important here that within an individual task no player was

able to produce 100% consistency. Between kicks within the task, the structure of the footwear,

the structure of the players foot, and therefore the homogeneity of the pressure distribution across

the anterior surface of the foot is consistent. But, the accuracy differed between tasks. Thus, the

homogeneity of the pressure distribution, as stated by Hennig as being the primary factor

influencing kicking accuracy, cannot explain this aspect of kicking accuracy, and therefore cannot

be the primary factor influencing kicking accuracy.

2.2.5 Summary of factors influencing kicking accuracy

The path of ball travel is governed by the laws of physics, and several authors have

estimated the flight path and outcome of a kick from the initial ball flight characteristics using

these (Atack, et al., 2015; Carré, et al., 2002). To kick accurately, players must have knowledge

(not necessarily explicit knowledge) of the forces applied to the ball during flight. Players can

and do exploit these ball flight laws to increase the chance of success for a task (Asai, et al., 2002;

Peacock, et al., 2017a).

Each foot-ball impact characteristic influences ball flight characteristics, but this

relationship has only been partially explored (Asai, et al., 2002; Ishii, et al., 2009, 2012; Peacock,

2013). Key factors such as impact location on the foot is only known to influence a few ball flight

characteristics, only because the full extent of the relationship has not been explored. Further, for

kicking codes that feature a non-spherical ball, such as rugby and Australian football, the

influence of ball orientation is also likely influential and should be explored.

Several researchers have attempted to identify factors that influence kicking accuracy

(Atack, et al., 2017; Dichiera, et al., 2006; Hennig, et al., 2009). However, systematic approaches

to identify the direct mechanisms influencing accuracy were not employed. Statements such as

‘the primary factor’ has been used, despite testing any other factor. Further, this factor does not

explain all instances of accurate and inaccurate kicking. Most importantly, it is not known why

players produce a breakdown of accurate and inaccurate kicks. Ultimately, all football coaches

38

should improve the breakdown of accurate and inaccurate kicks produced by their players, which

can only be determined once the mechanisms determining kicking accuracy have been

established.

2.3. Methodological approaches to analysing foot-ball impact

2.3.1 Analysis of human kickers

The analysis of football kicking has primarily been performed by taking observations of

a group and attributing differences in technique to the changes in performance outcomes. This

approach of analysing groups, however, may have concealed how certain impact characteristics

influence the outcome of the task. Previous group analyses have included comparisons between

different conditions and player cohorts (such as senior and junior players, preferred and non-

preferred limbs, different kicking tasks, and comparisons of footwear designs) and analyses

between individuals within a group (Asami & Nolte, 1983; Ball, et al., 2010; Nunome, et al.,

2006b; Peacock, et al., 2017a; Shinkai, et al., 2009; Shinkai, et al., 2013; Smith, et al., 2009;

Sterzing & Hennig, 2008). The limitations of a group analysis are (1) the inability to assess

changes in technique of one individual and (2) anatomical and technique differences between

players might also conceal differences in performance. For example, as mentioned previously,

the observed difference in foot-ball speed ratio between the junior and senior players by Ball, et

al. (2010) was likely not due to solely the difference in change in ankle plantarflexion, but also

the physical mass as this is known to influence impact efficiency (Andersen, et al., 1999).

The limitations of group analyses, however, do not encompass all possible analysis

approaches of human kickers. Experiments can alternatively be designed to make comparisons

within an individual, such as testing a player to perform multiple repetitions of a singular task.

Single-subject designs are still limited as the results from one individual cannot be inferred to a

larger group. However, this limitation can be eliminated by performing the individual analysis

across several participants and drawing conclusions from a group. This approach does require a

larger amount of work (as the number of overall trials analysed is greater), however, is appropriate

when the research question necessitates it. In football kicking, where the changes in impact

39

efficiency are influenced by the physical size of different players and the technique of an

individual, requires this methodological approach.

2.3.2 Mechanical kicking machines

Mechanical kicking machines have also been employed to explore how foot-ball impact

influences kick outcome measures (Flemmer & Flemmer, 2015; Fraser, Harland, Donovan, &

O'Shea, 2012). Mechanical kicking machines, and further extended to mechanical tests such as

ball drops, have been shown to produce far more stable outcomes than testing human kickers

directly (Flemmer & Flemmer, 2015). The ability to produce stable executions enables the ability

to directly assess the influence of one parameter on outcome measures. For example, Holmes

(2008) identified impacting the ball on the point and the belly produced a different coefficient of

restitution.

Attempts have also been made to isolate the influence of an individual parameter with

human kickers, where (Ishii, et al., 2012) used a cone to elevate a soccer ball off the ground to

assist in testing impact location across the proximal-distal direction. A similar strategy could also

be employed to test the influence of ball angle in rugby place kicking, by placing the ball at

different angles on the supporting tee. However, in kicking codes where the ball is not stationary

prior to impact (such as drop punt kicking), it is not possible to precisely control these conditions

at the beginning of impact. Furthermore, a consideration for all human kicking, is that an

individual may alter their technique based on these conditions at the beginning of impact.

Highlighting this, Ishii, et al. (2012) included normalised ball velocity, not ball velocity, in their

mathematical model likely because players varied their foot velocity under different kick

conditions. The dynamical behaviour of humans provide difficulty in determining the influence

of one individual factor.

2.3.3 Theoretical models & computer simulations

Theoretical models and computer simulations have also been used to determine the

influence of individual impact characteristics on outcome measures. Several theoretical models

40

to predict ball velocity have been developed and validated for soccer kicking (Andersen, et al.,

1999; Ishii, et al., 2009, 2012). Finite element analysis, a computer simulation approach, was used

to determine how impact location across the medial lateral direction of the foot influenced ball

spin and ball speed in soccer kicking (Asai, et al., 2002). These theoretical models and computer

simulations were all found to produce ‘agreeable’ results to the collected experimental data,

enabling further analysis of the developed methods to predict how performance can be improved

through manipulating individual components constructing the model. Importantly, the

‘agreeability’ of the results was subjectively determined.

Future work is required before the adaption of a theoretical model is applied to kicking a

non-spherical ball. A common thread of these theoretical models and simulations is the shape of

the ball used: the spherical soccer ball. Given the angle of an ellipsoidal ball has been shown to

influence coefficient of restitution (Holmes, 2008), this provides a level of complexity for

developing a model for an ellipsoidal ball. The inclusion of the ellipsoidal ball requires an

expansion of a new theoretical model – such as the oblique impact theory – to accommodate the

influence of ball angle. However, it is not yet known if the oblique impact theory is applicable to

football kicking. Furthermore, rather than developing a theoretical model which predicts the

outcome, a more robust approach is to experimentally assess an individual parameter by using a

mechanical kicking machine.

41

Chapter 3: Study 1 - The impact phase of drop punt kicking:

validation and experimental data of a mechanical kicking limb

This chapter was presented at the 34th International Conference of Biomechanics in Sport

(2016) and has undergone the peer review process.

Abstract: The purpose of this study was to validate a mechanical kicking limb and

analyse changes in foot speed on impact characteristics of drop punt kicking. Foot

speed was recorded as 9.1 – 21.2 m/s, and covered a range of kick distances. Ball

speed (13.0 – 29.7 m/s), contact distance (10.7 – 20.2 cm) and contact time (14.75 –

11.75 ms) were comparable to drop punt kicking. Impact efficiency (F:B ratio = 1.37

– 1.48, coefficient of restitution = 0.66 – 0.79) were high, caused by near perfect

rigidity in the design of the limb. Overall, the limb was found to be a valid

representation of a human performer. Foot speed displayed significant relationships

with ball speed (r = 0.998), contact time (r = -0.89), contact distance (r = 0.99) and

F:B ratio (r = -0.694). The relationship between foot speed and COR (-0.347) was

not significant.

42

3.1. Introduction

The human limbs (hands, feet) are frequently used among ball sports to strike the ball at

a specific location directing it onto a desired flight path (i.e. volleyball ‘spike’, football ‘kick’).

Across the football codes, the execution of the entire kicking skill differs due to the shape of the

ball used and the constraints of performing each kick. For example, a spherical ball is kicked off

the ground in soccer and an ellipsoidal ball is dropped from the hand prior to impact in drop punt

kicking.

Impact phase research has, for the most part, yielded similar results but with some notable

exceptions. Despite the different executions of the skills, four phases through the impact phase

have been identified with similar patterns reported in soccer and drop punt kicking (Peacock, et

al., 2017a; Shinkai, et al., 2009). On the other hand, relationships between some impact

characteristics have not been consistent across the codes. An increase in foot speed has been

linked to decreased contact time in soccer kicking (Nunome, et al., 2014). For drop punt kicking,

this relationship has been similarly found in one comparison of kicking tasks (Peacock, 2013),

but has not been found in other comparisons (Ball, 2008b; Ball, et al., 2010; Smith, et al., 2009).

Further, foot to ball speed ratio (F:B ratio) is considered a good measure of impact efficiency and

a medium, positive relationship has been identified with ankle rigidity (Shinkai, et al., 2013). It

is somewhat expected F:B ratio and ankle rigidity are linked due to relationships between

increased rigidity and ball speed in another soccer kicking study (Asami & Nolte, 1983). For drop

punt kicking however, comparisons of kicking groups found the measure to not differ

significantly when rigidity was increased (Ball, et al., 2010; Peacock, 2013).

Mechanical testing is an important addition to analyse the impact phase. An increased

variability is expected between kicking trials of performer-based studies, particularly in drop punt

kicking due to the execution in the skill where the ellipsoidal ball is dropped from the hand prior

to impacting the foot. Mechanical testing will allow for the isolation of specific variables so a

methodical exploration is made available if found to be valid, and thus should be used in

conjunction with performer-based studies. The aim of the present study was to validate a

43

mechanical kicking limb by using previous literature and analyse changes in foot speed on impact

characteristics during punt kicking.

3.2. Methods

A mechanical kicking limb performed punt kicks using a standard AF ball (Sherrin

‘Match Ball’, inflation: 69 kPa). Limb construction was based off information found in the

literature, including just the shank and foot segments rotating about a fixed point representing the

knee. These lower limb segments were found to be most influential during the impact phase, and

so the thigh was not included (Andersen, et al., 1999; Ball, 2008a). The shank was constructed

from a metal frame, with length (0.455 m) and mass (5.8 kg) similar to a typical AF player (height

= 1.85m, mass = 85kg) (Winter, 1990). The shape of the impacting object has been identified to

influence impact characteristics (Andersen, et al., 2008), so to obtain the correct foot impacting

area, impact location on the ball and relative foot-to-ball angle, a human foot was scanned and

printed as a rigid body whilst in a plantar-flexed position (Peacock, 2013) and attached to the

shank (further details on limb construction can be found in Section 4.2. ).

The limb was validated by using the results found in the literature of AF and soccer

kicking and a range of foot speeds were generated while keeping all other impact characteristics

constant across the kicking trials. Three reflective markers were attached to both foot and ball.

Data points were tracked at 4,000 Hz from three high speed video cameras (Photron SA3 and

MC2, Photron Inc., USA) and reproduced in 3d using ProAnalyst (Xcitex Inc., USA) and

Visual3d software (C-Motion Inc., USA). A low pass Butterworth filter of 280Hz smoothed all

data (Peacock, 2013). Impact characteristics were calculated using Matlab software (The

Mathworks Inc., USA). Pearson’s correlation calculated the relationship between foot speed with

impact characteristics.

The centre of the foot and ball were treated as a virtual landmark based off their tracking

markers (Peacock, et al., 2017a). Using these virtual landmarks, foot and ball speed were averaged

over five frames before and after impact. F:B ratio and coefficient of restitution (COR) were

44

computed using these measures (Andersen, et al., 1999; Peacock, et al., 2017a). Contact time was

visually identified using from one of the high speed video cameras located perpendicular to

impact (Peacock, et al., 2017a; Shinkai, et al., 2009). Contact distance was measured by the

distance the centre of the ball travelled from contact to release (Ball, 2008b). Effective mass was

calculated using conservation of momentum equations (Shinkai, et al., 2013).

3.3. Results

The mechanical limb generated a range of foot speeds between 9.1 to 21.2 m/s. Ball speed

was 13.0 – 29.7 m/s, and correlated significantly with foot speed (r = 0.998, Figure 3.1A). Contact

distance was 10.7 – 20.2 cm and correlated significantly with foot speed (r = 0.990). Contact time

was 14.75 – 11.75 ms, and correlated significantly with foot speed (r = -0.890). Foot to ball speed

ratio (Figure 1B) was 1.48 – 1.39 and correlated significantly with foot speed (r = -0.694). Though

not significant, COR (0.75 – 0.67) displayed a moderate relationship with foot speed (Figure 3.1B,

r = -0.347). Effective mass was calculated to be 2.29 ± 0.19 kg across the kicking trials.

3.4. Discussion

The foot speeds recorded are similar to performers’ kicks of varying distance. The foot

speed of drop punt kicking has ranged from 17.7 m/s for 20m kicks and 22.1 m/s for maximal

distance (Peacock, 2013). The 17.7 m/s recorded for 20m kicks in Peacock (2013) were also

considered high for the kick distance, due to a task specific strategy by the elite performers to

A B

Figure 3.1: Correlations between foot speed with ball speed (A), F:B ratio (B, black round ticks,

primary axis) and COR (B, grey square ticks, secondary axis).

45

maximise accuracy. The foot speeds of the present study (9.1 to 21.2 m/s) are therefore considered

representative of kicks ranging in distance from 10 to 60 m (maximal distance), and the limb was

successfully designed to cover a range of kick distances.

The impact characteristics indicate the mechanical limb was a very close representation

of a human performer during the impact phase. Ball speed, contact time, contact distance and

effective mass were similar to those recorded in AF (Table 3.1), however, F:B ratio was slightly

higher. In soccer kicking where performers had a calculated effective mass comparable to that of

the present study, F:B ratio was found to be in the range of 1.37 – 1.53 (Shinkai, 2013). These

values are very similar to that of the present study, and indicate the mechanical limb was almost

a perfect representation of the impact phase with only F:B ratio being slightly higher.

Table 3.1: Summary of impact characteristics across the literature of AF kicking.

Study Ball speed

(m/s)

Contact

distance (cm)

Contact time

(ms)

Effective

mass (kg)

F:B ratio

Present study 13.0–29.7 10.7–20.2 14.75–11.75 2.29 ± 0.19 1.48–1.39

Peacock

(2013)

22.1 ± 1.1 20.3 ± 2.4 13.2 ± 1.4 2.39 ± N/A 1.25 ± 0.04

Peacock

(2013)

28.1 ± 2.5 22.8 ± 2.9 12.1 ± 1.3 2.04 ± N/A 1.28 ± 0.06

Smith et al.

(2009)

32.6 ± 4.4 22 ± 2 11.53 ± 1.25 N/A 1.23 ± 0.11

The slightly higher value of F:B ratio is considered to be due to two factors of the limb’s

design. Firstly, there was no rotational displacement about the ankle and; secondly, there was no

shoe attached to the foot. This indicates the limb represented near perfect rigidity throughout the

impact phase. Future designs should consider implementing reduced rigidity about the ankle and

foot, to analyse ankle motion strategies (Peacock, 2013).

Foot speed correlated almost perfectly with ball speed and contact distance. Previous

comparisons of kick distances have displayed ball speed and contact distance to increase with

foot speed (Ball, 2008b; Peacock, 2013). As expected, this shows increases in foot speed should

be made by players to increase ball speed if they are able to keep all other impact characteristics

46

constant. The increased contact distance was possibly caused by greater deformation of the ball,

but, this was not measured. As noted by Nunome, et al. (2014), a method to calculate the

deformation of an ellipsoidal shaped ball should be developed to substantiate this claim.

Impact efficiency, as indicated by F:B ratio, decreased as foot speed increased. Contrasts

exist in the literature of F:B ratio in comparisons of drop punt kicking. Though ankle rigidity was

not analysed in this study, the studies by Ball, et al. (2010) and Peacock (2013) reported a

significantly larger foot speed in the conditions of increased ankle rigidity, and thus a two-fold

effect may have taken place: increased foot speed would have decreased F:B ratio, but an

increased ankle rigidity may have increased F:B ratio. To confirm this hypothesis, future studies

should analyse the link between ankle rigidity and impact efficiency while variability in foot

speed is minimised.

Although not significant, the relationship between foot speed and COR was negative with

a medium effect. A previous analysis using a pendulum to analyse the impact of soccer kicking

reported COR decreased with increases in pendulum speed (Andersen, et al., 2008). Further, this

negative relationship between foot speeds and COR is found in other impacts of sporting codes

(Cross, 2013). This literature suggests a negative relationship between foot speed and COR should

exist, however the cause behind the non-significance of this relationship could not be explained

by the results calculated. Possibilities may include the aging effect of the ball or variances in

manually placing the ball on the kicking tee between trials, however further work is required.

Contact time decreased as foot speed increased, a similar mechanism to soccer kicking

(Nunome, et al., 2014). This has been previously identified in a comparison of accuracy and

maximal distance drop punt kicks (Peacock, 2013), however, dissimilar results have been reported

in other comparisons (Ball, 2008b; Ball, et al., 2010; Smith, et al., 2009). The exact reasoning

behind the mixed results of drop punt kicking is beyond the scope of this study, but a high

variability can exist between trials and possibly influenced these previous studies. The results of

the present study and Peacock (2013) indicate the relationship between foot speed and contact

47

time is not specific to just soccer kicking, but also punt kicking. This also highlights the need to

conduct more mechanical testing due to the ability to investigate individual parameters.

3.5. Conclusions

This study successfully validated a mechanical kicking limb and analysed the change in

foot speed on impact characteristics. The design of the limb was found to be a very close

representation of a human performer during drop punt kicks of various distances, and future

designs should consider implementing reduced rigidity about the ankle and foot to decrease

impact efficiency. Foot speed was found to produce relationships with the measured impact

characteristics, excluding COR.

3.6. Acknowledgements

The authors would like to thank: Mick Küsel (Küsel Designs) for his work in the

development and construction of the mechanical limb and; Caleb Brockwell and Brandon Defina

for their assistance throughout the study.

3.7. Contribution of individual chapter to overall thesis

Each aim answered in the present chapter contributed toward the overall thesis. Aim 1,

of validating the mechanical kicking machine, identified the mechanical kicking machine

represented the human limb. The mechanical kicking machine was used again in Chapter 4, 5, 6

and 9. Aim 2, of performing a systematic exploration of foot speed, identified the efficaciousness

of performing a systematic exploration of impact characteristics with the mechanical kicking

machine. The high correlations found between foot speed and ball speed, contact distance and

contact time (each above a correlation of r = 0.88) support the ability to perform a systematic

exploration of impact characteristics with the mechanical kicking machine. The methodology of

performing a systematic exploration with the mechanical kicking machine was used in Chapter 4,

5 and 6.

48

Chapter 4: Study 2 - The relationship between foot-ball impact

and flight characteristics in punt kicking

This chapter has been published in Sports Engineering, Volume 20, Issue 3, pp 221-230

and has undergone the peer-review process. The published version of the manuscript is in

Appendix B.

Abstract: In football kicking, a player imparts the initial flight characteristics by

impacting the ball with their foot. Imparting the correct combination of flight

characteristics is the basis of a successful kick. However, examination of the

relationship between foot-ball impact with flight characteristics for a non-spherical

ball, the ball shape in Australian football and rugby, has been limited to ball velocity.

Consequently, little is known of the relationship with other flight characteristics of

ball trajectory and spin. The aim of this study was to determine the relationship

between impact and initial ball flight characteristics. A mechanical limb, designed

to replicate the impact phase of Australian football, performed punt kicks. Four

impact characteristics were systematically examined to determine their influence on

flight characteristics: foot velocity, medial-lateral impact location, proximal-distal

impact location and ball orientation. This study identified each flight characteristic

(ball velocity, elevation angle, azimuth angle and spin rate) was influenced by

multiple impact characteristics (foot velocity, ball orientation and/ or impact

location). For example, elevation angle was increased by foot velocity, relative foot-

ball orientation and proximal-distal impact location on the foot. Foot velocity had

the largest influence on ball velocity (linear slope = 1.43). Medial-lateral impact

location had the largest influence on azimuth angle (linear slope = 2.73). Ball

orientation had the largest influence on elevation angle and back-spin rate, both

measures were sine dependent (elevation angle curve amplitude = 19.4°; back-spin

49

rate curve amplitude = 2754°/s). Players must control all impact characteristics to

successfully kick to their desired destination.

50

4.1. Introduction

Impact forms one of many fundamental skills for ball sports. Across the football codes,

kicking is considered one of the most important skills of the game (Ball, 2008a). Players impart

ball flight characteristics by impacting the ball with their foot to achieve a desirable outcome,

such as scoring goals and passing the ball to fellow team members. There are multiple

combinations of flight characteristics that can achieve the same outcome for a kick. For example,

a consistent flight distance can be achieved by increasing the velocity and decreasing the

trajectory (assuming the trajectory is below the optimum angle based off the projection height).

Within gameplay however, there are specific flight characteristics that can increase the

chance of success for a kick. Impacting the ball at a higher velocity can enable shots at goal to be

taken from further distances and reduce the likelihood of interception from opposition by

decreasing flight time. Players can actively alter ball velocity and kick distance by changing

impact characteristics. The most notable mechanism for players to change ball velocity is to

control foot velocity before contact. The relationship between foot velocity and ball velocity has

been identified in several experiment designs (Ball, 2008a; Ball, et al., 2010; Peacock, et al.,

2017a; Smith, et al., 2009). Players can also increase ball velocity by increasing rigidity within

the ankle joint and foot segment (Ball, et al., 2010; Peacock, et al., 2017a; Sterzing & Hennig,

2008), and altering footwear characteristics such as mass and stiffness (Amos & Morag, 2002;

Hennig & Sterzing, 2010; Sterzing & Hennig, 2008).

While ball velocity is an important characteristic in gameplay situations, a player must

control all flight characteristics to reach a desired destination. The flight path, and therefore the

destination, is influenced by the initial trajectory, spin direction and spin rate due to their influence

on aerodynamic properties of air resistance and lift force (Alam, et al., 2009; Carré, et al., 2002;

Goff, 2013). Furthermore, players can purposely impart a spin as the curve of a ball in flight can

open the angle of goal and avoid interception from the opposition. When impacting a spherical

ball (such as soccer), spin qualities are influenced by impact characteristics of foot velocity, the

51

distance between the ball centre and the line of force applied to the ball, attack angle of the foot

and the coefficient of friction between the foot and the ball (Asai, et al., 2002; Ishii, et al., 2009).

For football codes that use a non-spherical ball, such as Australian Football (AF) and

rugby league (RL) that feature an ellipsoidal shape ball, little experimental data exists for impact

characteristics influential to flight characteristics other than the relationship between foot and ball

velocity (Ball, 2010; Peacock, et al., 2017a). Studies have analysed impact characteristics (Ball,

et al., 2010; Peacock, et al., 2017a; Smith, et al., 2009), initial flight characteristics (Holmes,

2008; Holmes, Jones, Harland, & Petzing, 2006), and aerodynamics (Alam, et al., 2009). For

example, Holmes (Holmes, 2008; Holmes, et al., 2006) identified the initial flight characteristics

of rugby kicking such as ball velocity and spin rate. But, these studies analysing kicking with the

ellipsoidal ball did not determine the relationship between foot-ball impact characteristics with

kick outcome or the initial flight characteristics. Thus, it is not known how players control the

flight path, and therefore the destination it reaches.

Oblique impact theory suggests spin qualities and flight trajectories are influenced by the

line of force application in respect to the ball centre of mass (Holmes, 2008). The findings of

spherical balls likely exist in kicking of an ellipsoidal ball. But, some of the most common types

of kicks used in AF and RL, drop punt and place kicking, are distinctly characterised by back-

spin about the short axis. The application of force (magntiude, direction, and point of application)

with respect to ball orientation, to obtain the back-spin, have different dynamics to that of kicking

a spherical ball. Therefore, the relationship between impact and flight of kicking an ellipsoidal

ball compared to a spherical ball will be different.

The aim of this study was to determine the relationship between impact and initial flight

characteristics featuring an AF ball (ellipsoidal shape). The impact characteristics of foot velocity,

medial-lateral impact location, proximal-distal impact location, and ball orientation were

systematically explored. Their relationship with initial flight characteristics of ball velocity,

trajectory (azimuth angle and elevation), and spin rate was determined.

52

4.2. Methods

A mechanical kicking limb performed drop punt kicks with a standard Australian Football

(AF) ball (‘Match Ball’, Sherrin, Australia) inflated to the Australian Football League

recommended pressure (69 kPa). The mechanical limb was developed to provide the ability to

systematically explore the effect of one impact characteristic on the outcome of the foot-ball

interaction without the influence of other characteristics. The striking limb comprised the shank

and foot (Figure 4.1) because previous studies had identified these to be influential during the

collision (Andersen, et al., 1999; Ball, 2008a; Ball, 2008b). Designed to replicate a typical AF

player, the shank was of metal construction comprising of two outer plates with a length of 0.455

m between the proximal and distal joints (based on an AF player’s average height = 1.85 m, and

using anthropometric data from Winter (1990) (Winter, 1990)). At the proximal end of the shank,

the ‘knee joint’ was modelled as a freely rotating axis to mimic flexion and extension. For the

foot segment, the foot and bottom part of the shank on the right side of a human that was 1.78 m

tall were three-dimensionally scanned whilst in a plantar-flexed position (the position adopted

during the kick) and printed as a three-dimensional object made of ABS plastic. To achieve the

appropriate length of the foot, the size of the scanned image was scaled up by the ratio of 1.85:1.78

based on the height of the person (1.78 m) and a typical AF player (1.85 m). The use of a human

foot was important as the shape of the contacting surface with the ball will influence impact

(Andersen, et al., 2005, 2008) and subsequent ball flight (Figure 4.2). For the purposes of this

study, the ‘ankle joint’ was locked so no movement occurred at the ankle and metatarsophalangeal

joints. These two segments were joined at the distal end of the shank with two plates fixed to the

medial and lateral sides of the foot, and designed so that no contact between these plates and the

ball occurred.

53

Figure 4.1: The mechanical limb

Figure 4.2: Foot segment attached at the distal point of shank

The rotating limb segment was powered by a counterweight via a pulley system that was

connected by the frame supporting the limb. Different foot velocity at ball contact were produced

by manipulating the starting point of the limb. The pulley system was designed for the

counterweights to cease applying torque to the rotating limb immediately before contact. For each

kicking trial, the ball was positioned on a kicking tee (Moose Kicking Tee Pty Ltd, Australia) that

was placed on a platform built into the frame. The tee allowed for a straight swing through of the

leg, typical of AF kicks (Ball, 2011), without any contact being made between the foot and the

tee. Adjustments could be made to the impact location moving the tee on the platform (for medial-

lateral), or adjusting the height of the platform in relation to the foot (proximal-distal). Because

the foot was rigid in construction, the orientation of the foot was unable to change and therefore

only ball orientation about the x-axis (see Figure 4.3 for ball orientation calculation) was required

54

to calculate relative foot-to-ball angle in the sagittal plane. Ball orientation about the x-axis was

adjusted by altering the position of the ball on the tee.

Figure 4.3: Reflective and virtual markers attached to the limb and ball

To analyse the impact phase, three high speed video cameras (Photron SA3 and MC2,

Photron Inc., CA USA) were synchronised, and recorded each trial at 4,000 Hz. Ball contact and

ball release were visually identified from the camera placed directly perpendicular to the direction

of the kick, and each video trial was cut down to 20 frames before and after impact. Three tracking

points were attached to the limb using 12.7 mm retro-reflective spherical markers (B & L

Engineering, CA, USA). Three tracking points were attached to the ball using a square piece of

reflective tape (25 x 25 mm) with a black circular sticker (radius = 8 mm) fixed to the middle (3M

Scotchlite 7610 reflective tape, 3M©, MN USA). These points were tracked in ProAnalyst

software (Xcitex Inc., MA USA) to generate three-dimensional coordinates with a root mean

square error of 0.9 mm. Calibration involved digitising 32 known points within a space of 0.12 x

0.45 x 0.3 m, which covered the entire capture field.

Visual3d software (C-Motion Inc., MD USA) reproduced virtual landmarks from a pre-

recorded static capture of the foot centre of mass (fCOM) based off three tracking markers

3 x ball tracking markers

3 x ball virtual markers

3 x foot tracking markers

fCOM virtual marker

Ball orientation about the x axis. Arrow indicates positive direction.

y, direction of kick

z

55

attached to the limb, and the ball geometric centre (bGC), top point of the ball and bottom point

of the ball from three tracking markers attached to the ball (Figure 4.3). All data were smoothed

with a low-pass, 2nd order Butterworth filter with a cut-off frequency of 280 Hz (Nunome, et al.,

2006b; Peacock, et al., 2017a). The fCOM was found at the midpoint between the lateral

malleolus and the head of the first metatarsal (Winter, 1990), however because the lateral

malleolus was not visible due to the construction of the limb, this point was approximated on the

dorsal surface of the foot (see Figure 3 for approximate location), and remained consistent

throughout the analysis. The bGC was calculated from the average position between two markers

attached to the top and bottom points of the ball captured during under static setting.

Impact and ball flight characteristics were calculated in Matlab software (The Mathworks

Inc., USA) (Figure 4.4). Foot and ball velocity were calculated from the first derivative of the

fCOM and bGC positional data averaged over five frames before and after contact. Impact

location in the medial-lateral direction was defined as the distance between the fCOM and bGC,

with positive values indicating a lateral displacement from the fCOM. Impact location in the

proximal-distal direction was defined as the distance between the bottom point of the ball and the

fCOM along the anterior surface of the foot, with positive values indicating a distal displacement

from the fCOM. Relative foot-to-ball angle was not calculated because the shape of the foot varied

pending on the area of impact on the foot. Rather, ball orientation about the x axis was calculated

and used as an indication of the relative foot-to-ball angle in the sagittal plane. Ball orientation

was calculated in the sagittal plane (Figure 4.3). Azimuth and angle of elevation were calculated

as the average of five frames after release from the foot (Figure 4.4). Back-spin rate was calculated

about the global x-axis. Foot-to-ball speed ratio, F:Bratio, was calculated from

𝐹: 𝐵𝑟𝑎𝑡𝑖𝑜 =

𝑣𝑏𝐺𝐶

𝑢𝑓𝐶𝑂𝑀 Equation 4.1

56

where, v was the final velocity u was the initial velocity. The coefficient of restitution,

CoR, was calculated from

𝐶𝑜𝑅 =

𝑣𝑏𝐺𝐶 − 𝑣𝑓𝐶𝑂𝑀

𝑢𝑓𝐶𝑂𝑀 Equation 4.2

Both foot-to-ball speed ratio and coefficient of restitution were used as measures of

impact efficiency, because foot-to-ball speed ratio has been used as a measure of impact efficiency

for the impact of AF kicking (Ball, et al., 2010; Peacock, et al., 2017a; Smith, et al., 2009), and

the coefficient of restitution quantifies the amount of energy lost during a collision and can

therefore also be considered a measure of efficiency.

Figure 4.4: Orthogonal reference system, approximate location of fCOM virtual marker

and parameter calculation of impact location on the foot, elevation angle and azimuth

angle. Arrows and angles represent positive directions.

The study examined foot velocity, medial-lateral impact location, proximal-distal impact

location, and relative foot-ball orientation in the sagittal plane. Each input measure was analysed

independently, where all remaining inputs were held constant. The baseline setting comprised a

foot velocity of 16.7 m/s, impact location in the medial-lateral direction of -1.15 cm from the foot

Elevation angle

Azimuth angle

Impact location

z

y, direction of kick x

fCOM virtual marker

57

centre of mass, impact location in the proximal-distal direction of 2.61 cm from the foot centre of

mass and ball orientation in the x-axis of 47.4°. Five trials were captured at this baseline setting

and used across all data sets. Kicks were performed in four datasets with all parameters held

constant within each dataset with the exception of the parameter of interest. For data set 1 (21

trials), foot velocity was varied from 9.1 – 21.2 m/s. For dataset 2 (17 trials), impact location in

the medial-lateral direction was analysed using a range of positions between -3.55 – 0.84 cm

across the foot centre of mass. For dataset 3 (17 trials), impact location in the proximal-distal

direction was analysed over a range of positions between -5.70 – 7.30 cm across the foot centre

of mass. For dataset 4 (28 trials), ball orientation about the x axis was analysed using a range of

positions between -11.6° to 85.3°.

A curve fitting procedure was used to identify the relationship between each impact

characteristic with each flight characteristic. The choice of curve fitted to the data was based on

two criteria: literature indicating previously identified relationships and theoretical models.

Visual inspection of plotted data and residual plots were screened to confirm if the plotted

relationship suited the data, and outliers were screened during this process. Linear relationships

were fitted to the systematic exploration of foot velocity. Linear relationships were fitted to the

relationship between medial-lateral impact location and azimuth angle and elevation angle, and

second order regressions were fitted to the relationship between medial-lateral impact location

and ball velocity and ball-spin rate. The choice of second order regression was based upon the

oblique impact theory. Linear relationships were fitted to the relationship between proximal-

distal impact location and ball flight characteristics, due to the linear increase in velocity of the

impact location with distal impact locations. For the exploration of ball orientation, a second

order regression was fitted to the relationship with ball velocity, a linear regression was fitted to

the relationship with azimuth angle, and a sine wave was fitted to the relationship for elevation

angle and back-spin rate due to the angular nature of ball orientation.

58

4.3. Results

Five outliers were removed from the foot velocity data set, thought to be due to a break-

in process of the ball and were removed from the remainder of the analysis. Foot velocity was

influential to all initial flight characteristics (Figure 4.5). Ball velocity (Figure 4.5: A), elevation

angle (Figure 4.5: C) and back-spin rate (Figure 4.5: D) increased linearly with foot velocity.

Azimuth angle decreased linearly with foot velocity (Figure 4.5: B). Impact efficiency measures

of foot-to-ball speed ratio and coefficient of restitution both decreased linearly with foot velocity

(Figure 4.5: E-F).

59

Figure 4.5: The relationships between foot velocity with ball velocity (A), azimuth angle

(B), elevation angle (C), back-spin rate (D), foot-ball speed ratio (E), and the coefficient of

restitution (F).

60

Medial-lateral impact location was influential to ball velocity, azimuth angle and back-

spin rate (Figure 4.6). Optimal relationships were identified between medial-lateral impact

location with ball velocity (Figure 4.6: A) and back-spin rate (Figure 4.6: C). Maximums were

identified at a medial-lateral impact location approximately -0.5 cm from the foot centre,

however, the dependence of ball velocity on impact location was low. Azimuth angle increased

linearly with impact location across the medial-lateral direction (Figure 4.6: B). Elevation angle

increased linearly with impact location across the medial-lateral direction (Figure 4.6: D), but the

magnitude of the slope was small suggesting low dependence.

Figure 4.6: The relationships between impact location across the medial-lateral direction

with ball velocity (A), azimuth angle (B), elevation angle (C), and back-spin rate (D).

Proximal-distal impact location was influential to ball velocity (Figure 4.7: A), elevation

angle (Figure 4.7: C) and spin rate (Figure 4.7: D), and all increased linearly with impact location

61

across the distal direction. A linear curve was fitted to proximal-distal impact location with

azimuth angle (Figure 4.7: B), and the magnitude of slope was small suggesting low dependence.

Figure 4.7: The relationships between impact location across the proximal-distal direction

with ball velocity (A), azimuth angle (B), elevation angle (C), and back-spin rate (D).

Ball orientation about the x-axis was influential to ball velocity, elevation angle and spin

rate (Figure 4.8). An optimal relationship was identified between ball orientation with ball

velocity (Figure 4.8: A), with a maximum identified at an orientation of approximately 43°. Sine

curves were fitted to the relationships between ball orientation with elevation angle (Figure 4.8:

C) and back-spin rate (Figure 4.8: D). A linear curve was fitted to the relationship between ball

orientation with azimuth angle (Figure 4.8: B), but the magnitude of slope was small suggesting

low dependence.

62

Figure 4.8: The relationships between ball orientation about the x-axis with ball velocity

(A), azimuth angle (B), elevation angle (C), and back-spin rate (D).

4.4. Discussion

A player must control flight characteristics for a kick to be successful. To date, little is

known of the relationship between foot-ball impact with all flight characteristics, the phase of

kicking when a player imparts the flight characteristics. Therefore, the aim of this study was to

determine the relationship between impact and ball flight characteristics through systematic

exploration.

4.4.1 Foot velocity

Ball velocity increased linearly with foot velocity (Figure 4.5: A). This linear relationship

was comparable to previous results (Andersen, et al., 1999; De Witt & Hinrichs, 2012; Kellis &

Katis, 2007). Andersen & colleagues (Andersen, et al., 1999) developed a model to predict ball

63

velocity from the angular momentum of the leg and coefficient of restitution, which indicated ball

velocity increased linearly with foot velocity. They found the results of soccer instep kicking

fitted the model appropriately. Similarly, group comparisons have identified increases in foot

velocity translated to increases in ball velocity (Peacock, et al., 2017a).

Foot velocity negatively influenced impact efficiency (Figure 4.5: E-F), but, the

magnitude of reduction had little overall effect on the relationship between foot velocity with ball

velocity. Negative linear relationships were identified between foot velocity with foot-ball speed

ratio and coefficient of restitution, a similar finding to previous analyses of inelastic objects in

collisions (Cross, 2013). Foot-ball speed ratio represents the slope of the linear relationship

between foot and ball velocity. Because foot-ball speed ratio was not constant, the relationship

between foot and ball velocity was not linear. Post-hoc curve fitting between foot velocity and

ball velocity with a power curve to represent the negative slope of foot-ball speed ratio also fit

the data well (equation: y = 1.599x0.962). But, a comparison of the power and linear curves over

the range of foot velocity that a player can produce (up to 26.5 m/s (Ball, 2011)) revealed a

minimal difference between the two curves (Figure 4.9). The linear curve adequately described

the dependence of ball velocity on foot velocity for the range of values a player can produce.

Figure 4.9: Post-hoc analysis of the relationship between foot velocity with ball velocity.

The solid line represents the linear curve, and the dashed line represents the power curve.

64

Back-spin rate increased linearly with foot velocity (Figure 4.5: D). The increase in back-

spin rate was caused from a combination of the magnitude of force applied to the ball and the

ellipsoidal shape of the ball with its orientation on the foot. The oblique impact theory indicates

spin generated during impact is created from a result of the moment that is applied to the ball

when the force vector does not pass through the centre of mass of the ball, and is proportionate to

the product of the magnitude of the force and the moment arm (Holmes, 2008). Across the foot

velocity dataset, the magnitude of force increased with foot velocity, increasing the moment

applied to the ball.

Foot velocity influenced the trajectory of ball flight (Figure 4.5: B-C), but each flight

component was influenced by different factors associated with an increased foot velocity.

Elevation angle increased linearly with foot velocity, due to a greater elevation trajectory of the

foot during foot-ball contact. The contact distance between foot and ball increased linearly with

foot velocity (post-hoc analysis; linear relationship; r2 = 0.989). As the foot was at the beginning

of the upward arc as it rotated about the knee, the elevation angle of the foot increased with the

increased contact distance. Azimuth angle decreased linearly with foot velocity, due to the

nonhomogeneous geometric properties of the foot. The trajectory of the ball in the azimuth

direction was determined solely by the geometric surface of the foot across the medial-lateral

direction. Oblique impact theory indicates the trajectory of the foot and the angle of foot surface

impacting the ball changes the angle of the force vector applied to the ball. The trajectory of the

foot was held constant for the present study and therefore was not influential. When foot velocity

increased, the surface impacting the ball changed. This was due to a two-step process. Firstly, an

increased foot velocity meant a greater area of the ball covered the foot. Secondly, because the

surface of the foot was asymmetrical about the proximal-distal axis, the force direction applied to

the ball across the azimuth dimension was speed dependent. This supports previous work that has

suggested designing footwear with a more symmetrical surface will be beneficial to a more

consistent ball flight, also associated with kicking accuracy (Hennig, 2011). A shoe was not

65

included in the present analysis due to the current design iteration of the mechanical kicking

machine used in the present study.

4.4.2 Impact location

Ball velocity and back-spin rate increased linearly as impact location moved distally

(Figure 4.7: A & D). The linear velocity of the impacting point increased as the impact location

was moved distally, increasing the force applied to the ball. However, continuing to move the

impact location distally has limitations. Firstly, there is an endpoint where if the impact location

was moved beyond the length of the foot, the ball would be partially or not impacted at all.

Secondly, a limitation of the analysis was that the ankle joint was fixed. Plantar flexion during

impact of AF kicking has been reported to range from 2.2° to 7.2° depending on the task (Ball, et

al., 2010; Peacock, et al., 2017a), and an increased ankle plantarflexion during impact has been

associated with decreased impact efficiency (Lees & Nolan, 1998). Furthermore, these studies

analysed kicks that were struck ‘well’. An impact towards the toe, while contacting the foot on

an aspect that is moving faster, will result in a greater moment arm tending to force the foot into

plantar flexion reducing the performance advantage may be lost. Future work should implement

reduced rigidity about the ankle when analysing impact location to determine the influence of

changes in rigidity on kick outcome.

Ball velocity and back-spin rate were maximum with a medial-lateral impact location of

0.5 cm from the foot centre (Figure 4.6: A & D). The results of Asai and colleagues (Asai, et al.,

2002) indicated an optimal relationship existed between impact location across the medial-lateral

direction with ball velocity in instep soccer kicking, and a similar mechanism was expected to

occur with back-spin rate. The results of the present study however, identified little reduction in

ball velocity and a moderate reduction in back-spin rate when impact location was moved either

medially or laterally from -0.5 cm from the foot centre. Asai and colleagues (Asai, et al., 2002)

observed a much greater reduction in ball velocity, reducing from 26.0 m/s to 0 m/s when impact

location was moved medially 16 cm, and to 6.2 m/s when moved laterally 16 cm. This reduction

occurred because of the distance the impact location was moved. The change in impact location

66

from foot centre for the present study was only -3.6 cm to 0.8 cm from the foot centre of mass in

the medial-lateral direction. Further changes of impact location from foot centre were limited by

the ball supporting the tee, because moving the impact location further would have resulted in the

foot impacting the tee and not impacting the ball cleanly, thus altering the impact conditions.

Moving impact location laterally increased azimuth angle linearly and had no influence

on elevation angle (Figure 4.6: B & C). These relationships can be explained by the shape of the

foot; as the impact location was moved laterally, the surface angle of the foot changed pointing

from the medial to lateral direction, which in-turn altered the ball flight trajectory to move from

the medial to lateral direction. Moving the impact location laterally had no effect on elevation

angle, because there was no change in the shape of the foot surface across this direction. Post-hoc

analysis revealed that angular velocity about the y-axis of the ball was linearly dependent upon

impact location across the medial-lateral direction, considered also to be due to change in angle

of the foot surface. This supports accuracy may be enhanced through footwear designs that

promote a more symmetrical surface.

Moving impact location distally increased elevation angle linearly and had no influence

on azimuth angle (Figure 4.7: B & C). The relationship between elevation angle with change in

the impact location in the proximal-distal direction was not due to the shape of the foot, but due

to the higher linear velocity at the impacting point. As the impact location was moved distally, a

higher linear velocity of the impacting point was applied to the ball, influencing the force vector

applied to the ball. Moving the impact location distally had no effect on azimuth angle because

there was no change in the surface angle of the foot.

4.4.3 Ball orientation about the x-axis

Ball orientation about the x-axis influenced back-spin rate and elevation angle (Figure

4.8: C & D). The sine curve fit the data well, outlining the dependence of these flight

characteristics on ball orientation about the x-axis. Holmes (Holmes, 2008) performed a ball drop

test to determine the influence of ball orientation on flight parameters, tested between the range

67

of 0° to 90°. Their results identified a sine dependence was likely to be present over a change in

ball orientation about the x-axis of 0° to 180°. We hypothesise the amplitude of both sine waves,

and the vertical midpoint of the elevation angle sine wave were dependent on the velocity and

elevation trajectory of the foot prior to impact. This is supported by the previous analysis of foot

velocity, where it was identified under a constant ball orientation, increasing foot velocity resulted

in an increase to ball velocity and elevation angle.

Ball velocity was maximum at a ball orientation about the x-axis of approximately 43°

(Figure 4.8: A). Holmes (Holmes, 2008) performed a bounce test and identified the coefficient of

restitution for an Australian Football ball was greater at the point compared to the centre. The

results of the present study support this finding, where ball velocity was greater when impacted

at the point (ball orientation of 65° = ball velocity of 24 m/s) compared to the centre (ball

orientation of -25° = ball velocity of 20 m/s). However, ball velocity was even higher when

impacted at 43°, the maximum ball velocity of 24.4 m/s.

4.5. Conclusion

This study systematically explored four impact characteristics of kicking an ellipsoidal

shaped ball to determine the relationship with initial flight characteristics. Each flight

characteristic was influenced by multiple impact characteristics. Ball velocity increased linearly

with foot velocity and proximal-distal impact location. Impacting the ball 0.5cm medially from

the foot centre, or with a ball orientation about the x-axis of 43° produced the highest ball velocity.

Azimuth angle increased linearly with foot speed and with medial-lateral impact location.

Elevation angle increased linearly with foot velocity and proximal-distal impact location. The

relationship between elevation angle with ball orientation about the x-axis followed a sine curve,

over the period of 180°. Back-spin rate increased linearly with foot velocity and proximal-distal

impact location. The relationship between back-spin rate with ball orientation about the x-axis

also followed a sine curve over the period of 180°.

68


Chapter 4 contributed toward the overall thesis by further exploring how individual foot-

ball impact characteristics influence ball flight characteristics. As identified in Chapter 3, the

mechanical kicking machine was identified to validly replicate the human limb and could be used

to perform a systematic exploration of individual foot-ball impact characteristics. The mechanical

kicking machine was used to perform the systematic exploration of individual foot-ball impact

characteristics. The number of foot-ball impact characteristics systematically examined, and the

number of ball flight characteristics assessed increased from Chapter 3. Foot velocity, impact

location and ball orientation were each examined and treated as independent variables. Ball

velocity, ball flight trajectory and ball spin, the chosen ball flight characteristics, were measured

and treated as dependent variables. The results from these systematic examinations contributed to

answering aims 1 and 2 of the overall thesis. Specifically, aim 1 was to identify how foot-ball

impact influenced impact efficiency. It was identified foot velocity, ball angle, and impact

location each influenced impact efficiency. Further discussion on how this chapter contributes to

aim 1 can be found in section 10.1. Aim 2 was to identify how foot-ball impact influenced ball

flight characteristics and kicking accuracy. It was identified foot velocity, ball orientation and

impact location each influenced ball flight characteristics. Further explanation of how this chapter

contributed to aim 2 can be found in section 10.2. One design feature of the limb was that it

featured a rigid ankle (i.e. no ankle motion). Ankle motion is an important factor influencing

kicking (Nunome, et al., 2006b; Peacock, et al., 2017a), and Chapters 5 and 6 explored the

influence of ankle motion via systematic exploration of impact characteristics with the mechanical

kicking machine.

69

Chapter 5: Study 3 - The influence of joint rigidity on impact

efficiency and ball velocity in football kicking

This chapter has been published in Journal of Biomechanics (in press) and has undergone

the peer-review process. The published version of the manuscript is presented in Appendix C.

Abstract: Executing any skill with efficiency is important for performance. In

football kicking, conflicting and non-significant results have existed between

reducing ankle plantarflexion during foot-ball contact with impact efficiency,

making it unclear as to its importance as a coaching instruction. The aims of this

study were to first validate a mechanical kicking machine with a non-rigid ankle,

and secondly compare a rigid to a non-rigid ankle during the impact phase of football

kicking. Measures of foot-ball contact for ten trials per ankle configuration were

calculated from data recorded at 4,000Hz and compared. The non-rigid ankle was

characterised by initial dorsiflexion followed by plantarflexion for the remainder of

impact, and based on similarities to punt and instep kicking, was considered valid.

Impact efficiency (foot-to-ball speed ratio) was greater for the rigid ankle (rigid =

1.16 ± 0.02; non-rigid = 1.10 ± 0.01; p < 0.001). The rigid ankle was characterised

by significantly greater effective mass and significantly less energy losses.

Increasing rigidity allowed a greater portion of mass from the shank to be used

during the collision. As the ankle remained in plantarflexion at impact end, stored

elastic energy was not converted to ball velocity and was considered lost. Increasing

rigidity is beneficial for increasing impact efficiency, and therefore ball velocity.

70

5.1. Introduction

Many ball sports involve a performer accelerating the ball by impacting it with a distal

body segment or piece of equipment. The outcome of this collision can be quantified by its initial

flight characteristics, such as velocity, spin and trajectory, because they all influence the flight

path of a projectile (Goff, 2013). Attaining a high ball velocity is a desirable characteristic for

performance, enabling the ball to travel further or to reach a target in a shorter time. In game

situations, this can reduce the possibility of interception from the opposition and provide more

opportunities for scoring from further distances. The velocity of the distal body segment (Kellis

& Katis, 2007; Lees & Nolan, 1998) or piece of equipment (Cross, 2011) immediately prior to

the collision is an important component for final ball velocity. However, the ability to produce a

high velocity can be limited by a players’ physical capacity, so impacting the ball with a higher

efficiency will generate a higher ball velocity for a given striking velocity.

In football kicking, where the foot impacts the ball, the ankle is passively plantar-flexed

during the collision due to the high forces and short impact duration of approximately 10 ms

(Shinkai, et al., 2009). A reduction in the forced plantarflexion has been associated with an

increase in ball velocity (Asami & Nolte, 1983; Peacock, et al., 2017a), by improving impact

efficiency from an increase in the effective mass (Kellis & Katis, 2007; Lees & Nolan, 1998).

Furthermore, it can also be considered that when the ankle remains in plantarflexion at the end of

impact, elastic energy stored within the joint is not converted to ball velocity and can therefore be

considered lost, and might cause a further reduction in impact efficiency. The relationship

between impact efficiency with effective mass and energy losses also has theoretical support; the

conservation of momentum combined with the coefficient of restitution (Equation 5.1) indicates

impact efficiency (foot-to-ball speed ratio) and ball velocity would be improved from an increase

in either the effective mass or coefficient of restitution.

𝑣𝑏 = (

1 + 𝑒

1 + 𝑚𝑏 𝑚𝑓⁄) ∙ 𝑢𝑓 + (



71



While some studies have identified a reduction in the forced plantarflexion to be

beneficial to kick performance, there are some that have observed non-significant findings with

small effect sizes or individual players questioning the association. Peacock, et al. (2017a)

identified a significantly different magnitude of plantar-flexion between distance and accuracy

kicks but impact efficiency was non-significant with a small effect, indicating a reduction in

forced plantarflexion may not be associated with impact efficiency. Furthermore, Nunome, et al.

(2006b) identified a player that produced a relatively high ball velocity also displayed a relatively

high plantar-flexion, again questioning the association of reduced plantar-flexion with impact

efficiency. Further to support no association between reduced plantarflexion with impact

efficiency, Shinkai, et al. (2013) stated that when the ball mostly impacted the foot on the centre

of mass, ball impact was most likely assumed to be a collision between the foot and ball, and

therefore motion of the ankle does not influence the outcome. This questions the coaching

instruction of attaining a firm ankle for kicking performance, and more generally the influence of

joint rigidity in sporting skills when attaining high ball velocity. Therefore, the aim of this study

was to determine the influence of plantarflexion during foot-ball impact on impact efficiency and

ball velocity.

To determine the influence of plantarflexion during foot-ball impact on impact efficiency,

a mechanical kicking machine with a rigid and a non-rigid ankle configuration was used. Kicking

is a dynamic skill where many characteristics can influence the outcome of a kick, therefore, a

methodology to control other impact characteristics, such as a mechanical kicking machine, was

warranted. The rigid setting of the mechanical kicking machine has already been validated

(Peacock & Ball, 2016), but not the non-rigid configuration. The first aim of the study was to

validate the ankle motion of the non-rigid ankle configuration. The second aim was to compare

the rigid and non-rigid ankle configurations.

72

5.2. Methods

5.2.1 Mechanical kicking machine with adjustable ankle rigidity

A mechanical kicking machine performed trials with an Australian football (AF) ball

(‘Sherrin Match Ball’, Russell Corporation, Scoresby, Australia; mass = 0.456 kg, inflation =

manufacturers recommendation and league requirement of 69 kPa) (Figure 5.1A). To replicate

drop punt kicking of elite AF players, the kick leg was constructed to match the length and mass

of the shank and foot, and foot shape of an AF player (height: 1.85m; mass = 85kg). This

mechanical kicking machine was used previously with a rigid foot segment and was found to be

a valid representation of drop punt kicking (Peacock & Ball, 2016).

Figure 5.1: A) The mechanical kicking limb. B) Ankle rotation design with controlled

rigidity via spring mechanism.

To analyse the influence of ankle rigidity on impact efficiency, a spring mechanism

resisting plantarflexion was added to the previously validated mechanical kicking machine

(Figure 5.1A). The spring mechanism was considered appropriate to represent the ankle motion

73

during impact, as both the spring and human ankle during impact are passive (Shinkai, et al.,

2009), where it is considered the initial conditions at the start of impact determine the phase

(Nunome, et al., 2006b). The leg configuration (Figure 5.1B) comprised two segments: a shank

and a foot segment. The shank segment was constructed of two metal plates (length = 0.455 m;

mass = 4.2 kg) that attached to the trigger mechanism of the kicking machine (leg and trigger

mass = 21.15 kg). While the mass of the trigger was high, it contributed little to the moment of

inertia because it was close to the axis of rotation. The foot segment was attached to the distal end

of the shank segment and plantar/dorsal ankle rotation occurred via two bearings. Because the

shape of the impacting surface influences the interaction (Andersen, et al., 2005, 2008), and

because the impacting area during drop punt kicking covers the bottom part of the shank

(Nunome, et al., 2014), the bottom part of the shank and entire foot of a human was 3d scanned

and integrated into the limb design. The foot segment was constructed by a 3d printer, made of

ABS plastic with a weight of 1.09 kg. It was assumed the foot acted as a rigid body during impact.

A football boot (Adidas Kaiser 5; mass = 0.364 kg) was placed on the foot segment. Overall, the

moment of inertia of the entire kick leg was estimated to be 0.71 kg.m2. It was assumed each body

were rigid during impact, the only motion was rotation about the knee and ankle joints.

By setting the ankle to be either rigid or non-rigid at the start of impact, this enabled a

direct comparison to determine the influence of ankle rigidity while all other impact

characteristics were held constant (foot speed, impact location, ball orientation, moment of inertia,

etc.). The rigid ankle was obtained by locking out rotation of the foot segment by inserting a bolt

between shank and foot segments (see insert of Figure 5.1B). The non-rigid ankle was obtained

by synthetic rope representing connective tissue and two springs representing elastic tissue within

the joint. The synthetic rope stemmed from the foot segment and passed across the anterior side

of the ankle joint, before connecting to two springs just below the knee joint (Figure 5.1B). The

torque preventing plantarflexion could be calculated by multiplying spring stiffness by the radius

of 40 mm (the displacement between the ankle axis of rotation and the contact point of the tendon

across the anterior aspect of the joint). It was assumed the synthetic rope did not stretch while the

74

ankle was forced into plantarflexion, enabling the linear deformation of the spring to be calculated

from the ankle plantar/dorsal flexion motion. To determine if the non-rigid ankle validly

represented ankle motion of human performers, the ankle motion of the mechanical limb was

compared to previous literature.

5.2.2 The initial conditions of impact for the comparison of ankle rigidity

The imposed initial conditions of impact were a foot velocity prior of 16.4 ± 0.2 m/s

across all trials, and spring force at the ankle joint of 950 N for the non-rigid setting (yielding a

torque preventing plantarflexion of 38 N.m). The angle of the rigid ankle was set at 155.6°, and

the angle of the non-rigid ankle was set at 156.8°. Impact location was set to impact the foot

approximately at its centre of mass. Pilot testing identified this setting to obtain a change in ankle

angle of approximately 8° plantarflexion, a similar value obtained in both AF (7.2 ± 2.2°) and

soccer (7.1 ± 5.8°) performer studies where the foot was passively plantarflexed during impact

(Peacock et al., 2017; Shinkai et al., 2009). Ten trials were recorded for each setting on the same

testing session using the same ball, and to minimise the possibility of order effects (given the ball

can ‘soften’) five trials were completed under the rigid setting, followed by 10 trials under the

non-rigid setting, and five final trials under the rigid setting.

5.2.3 Data collection

Two-dimensional sagittal plane data were measured through high-speed video camera

(Photron SA3, Photron Inc., USA, 4,000 Hz, resolution 768 x 512 pixels) zoomed in to include

just the kicking area. Tracking markers (12.9 mm spherical and 8 mm flat) on the limb and ball

were tracked from 20 frames before ball contact to 20 frames after the ball had left the boot

(identified visually from the video) using ProAnalyst software (Xcitex Inc., Woburn MA, USA).

To eliminate movement of the boot influencing foot and ankle data, the foot tracking marker was

attached directly to the fifth metatarsal by cutting a hole in the boot and tapping a thread into the

foot. This marker was also occluded for approximately 10 frames through the middle of the

tracking stage as it passed through the tee supporting the ball, and these points were interpolated

75

within the tracking software. The interpolation feature was considered suitable because there was

no change in direction of the marker during this period.

5.2.4 Data analysis and parameter calculation

Raw X and Y coordinates were exported to Visual3d software (C-Motion Inc.,

Germantown MD, USA) to be analysed with a custom-made pipeline. Firstly, four virtual markers

were derived from the three tracking markers of the foot using the method from (Peacock et al.,

2017). These virtual markers were on the anterior aspect of the foot, and were found at the top of

the shank segment (ShT), bottom of the shank segment (ShB), centre of the foot (FC) and bottom

of the foot (FB) (Figure 5.2). All parameters were calculated within Visual3d and Microsoft Excel

(Microsoft Corporation, Redmond WA, USA) software from the measured X-Y coordinate data.

Foot and ball velocity were calculated from the first derivative of X-Y coordinate data, and were

smoothed with a low-pass Butterworth filter at a cut-off frequency of 170 Hz. The choice of cut-

off filter was based upon three criteria: discrete Fourier Transform analysis looking at different

cut-offs between 10 to 400 Hz, visual inspection of the signals at different cut-offs and previous

literature (Nunome et al., 2006; Peacock et al., 2017; Shinkai et al., 2009). Initial and final velocity

of foot and ball were averaged over five frames.

76

Figure 5.2: Orthogonal reference and tracking and virtual markers of the limb and ball.

Virtual markers are represented by the grey outline of the circular markers.

The energy sources of interest were the kinetic energy of the ball and the elastic energy

stored in the springs preventing plantarflexion of the ankle. Linear kinetic energy of the ball was

quantified from its mass and linear velocity (Equation 5.2). Rotational energy was quantified from

the angular velocity and moment of inertia (Equation 5.3 and Equation 5.4). Energy stored in the

spring mechanism preventing plantarflexion was quantified from its deformation (Equation 5.5

and Equation 5.6). The sum of ball and ankle energy included translational and rotational kinetic

energy and the energy stored within the spring mechanism (although not applicable to the rigid

ankle).

𝐵𝑎𝑙𝑙𝐾𝐸,𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛𝑎𝑙 (𝐽) = 12⁄ ∙ 𝑚𝑏 ∙ 𝑣𝑏

2 Equation 5.2

77

𝐵𝑎𝑙𝑙𝐾𝐸,𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 (𝐽) = 12⁄ ∙ 𝐼𝑏 ∙ 𝜔𝑏

2 Equation 5.3

Where Ib = Inertia of the ball, calculated from Equation 5.4; ω = angular velocity.

𝐼𝑏 =

𝑚(𝑅𝑎2 + 𝑅𝑏

2)

5 Equation 5.4

Where Ra = the short radius of the ball; Rb = the long radius of the ball

𝑑 = (𝐷𝑖 +

∆𝐴𝐴

180∙ 𝜋 ∙ 𝑅𝑡) Equation 5.5

Where d = spring deformation; Di = initial spring deformation (m), ΔAA = change in ankle

angle (degrees), Rt = radius of tendon across ankle joint (m).

𝐴𝑛𝑘𝑙𝑒𝐸𝐸 (𝐽) = 12⁄ ∙ 𝑘 ∙ 𝑑2 Equation 5.6

Where k = spring stiffness; d = spring deformation, as calculated from the limb settings

and change in ankle angle.

Impact efficiency measures of foot-to-ball speed ratio, coefficient of restitution and

effective mass are presented in Equation 5.7, Equation 5.8, Equation 5.9.

𝐹: 𝐵 𝑅𝑎𝑡𝑖𝑜 = 𝑣𝑏

𝑢𝑓 Equation 5.7

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𝐶𝑂𝑅 = 𝑣𝑓 − 𝑣𝑏

𝑢𝑓 Equation 5.8

𝐸𝑀 (𝑘𝑔) =𝑚𝑏 ∙ (𝑣𝑏 − 𝑢𝑏)

𝑣𝑓 − 𝑢𝑓 Equation 5.9

5.2.5 Statistical analysis

A two-tailed, two-sampled equal variance T-test was performed and effect sizes were

calculated. The P-value was set at 0.05 to indicate significance and effect sizes were defined as:

d < 0.2 = none, d < 0.5 = small, d < 0.8 = medium and d > 0.8 = large (Cohen, 1988). A Holm’s

correction was applied to reduce the likelihood of type 1 statistical errors (Holm, 1979).

5.3. Results

5.3.1 Validation of mechanical limb segment

The non-rigid ankle was in dorsi-flexion for the first 31% of impact duration, followed

by distinct plantar-flexion for the remainder of impact (Figure 5.3). The total change in ankle

angle between ball contact and ball release was 8.2 ± 0.7° and the total impact duration was 10.7

± 0.3 ms.

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Figure 5.3: Non-rigid ankle motion through impact (± standard deviation). The flat black

line represents ankle angle at impact start, plotted throughout the duration of impact as a

reference to the change in angle during impact.

5.3.2 Comparison of ankle rigidity settings

Foot to ball speed ratio, ball velocity and translational kinetic energy of the ball were

significantly greater under the rigid ankle (Table 5.1). The effective mass of the striking limb was

greater under the rigid ankle; effective mass as calculated through the conservation of momentum

was greater for the rigid ankle, and although the elastic energy in the ankle for the rigid setting

was naught, the sum of ball kinetic energy and ankle elastic energy were equal under the rigid

and non-rigid ankle settings despite a smaller reduction in foot velocity under the rigid ankle.

Energy losses during the collision were significantly greater under the non-rigid ankle; coefficient

of restitution was greater under the rigid ankle and 6.3 ± 0.6 J of elastic energy was stored in the

spring mechanism at the end of impact as the ankle remained in plantarflexion.

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Table 5.1: Kick impact characteristics.

Rigid Non-rigid T-test Holm's Corrected

P-value threshold

Effect size

Value (Cohen's d) Classification

Foot to ball speed ratio 1.16 ± 0.01 1.11 ± 0.01 p < 0.001* 0.007 1.79 Large

Ball velocity (m/s) 19.0 ± 0.3 18.3 ± 0.2 p < 0.001* 0.013 1.61 Large

Translational kinetic energy of ball (J) 82.3 ± 2.5 76.7 ± 1.5 p < 0.001* 0.017 1.60 Large

Effective mass (kg) 2.1 ± 0.1 1.7 ± 0.1 p < 0.001* 0.008 1.72 Large

Σ ball kinetic and ankle elastic energy (J) 88.6 ± 2.5 89.1 ± 1.3 p = 0.32 0.050 0.22 Small

Reduction in foot velocity (m/s) 4.1 ± 0.2 4.8 ± 0.3 p < 0.001* 0.010 1.63 Large

Coefficient of restitution 0.42 ± 0.01 0.40 ± 0.02 p = 0.01* 0.025 0.96 Large

Change in ankle angle (°) - 8.3 ± 0.7 - - - N/A

Energy stored in ankle (J) - 6.3 ± 0.6 - - - N/A

*denotes significance

81

5.4. Discussion

5.4.1 Validation of non-rigid ankle limb configuration

Kicking is a dynamic skill where many impact characteristics, if not accounted for, can

influence the outcome of a kick. Therefore, to determine the influence of one characteristic on

kick outcome, specifically ankle plantarflexion for the present study, a mechanical kicking

machine with the ability to control ankle motion was developed. The first aim of the present study

was to validate the non-rigid ankle motion by comparing to previous research.

The passive motion of the non-rigid ankle was representative of human ankle motion

during drop punt and instep soccer kicking based on similar motion of the ankle during impact,

overall change in ankle plantarflexion, and contact time. The ankle was in dorsiflexion for the

first 31% of impact duration, followed by distinct plantarflexion for the remainder. This ankle

movement pattern was similar to both drop punt and instep kicking, where both Peacock, et al.

(2017a) and Shinkai, et al. (2009) identified the majority of analysed players within the tested

groups produced a similar pattern. The overall change in ankle plantarflexion was 8.2 ± 0.7°, a

comparable value to both drop punt kicking (7.2 ± 2.2°) and soccer instep kicking (7.1 ± 5.8°)

(Peacock, et al., 2017a; Shinkai, et al., 2009). Further, the overall contact time (10.7 ± 0.3 ms)

was consistent with human kicking values of both the drop punt (13.2 ± 2.2 ms) and soccer instep

(9.0 ± 0.4 ms) kicks (Peacock, et al., 2017a; Shinkai, et al., 2009). Based on these similarities, it

can be concluded the ankle motion of the mechanical kicking machine validly represented human

football kicking. This result supports ankle motion during impact as being passive, as the ankle

motion was validly replicated by a spring mechanism that was passive in motion.

5.4.2 Comparison of rigid to non-rigid ankle

During impact the ankle is forced into passive plantar-flexion due to the high forces and

short time of the interaction (Shinkai, et al., 2009). Contrasting results exist as to whether impact

efficiency is improved when reducing this plantarflexion. Therefore, the aim of this study was to

compare a rigid and a non-rigid ankle while all other impact characteristics were held constant.

82

The key results were that impact efficiency was greater under the rigid ankle, due to an increase

in effective mass and decrease in energy losses.

A more rigid ankle increases the effective mass of the striking limb compared to a less

rigid ankle, where a greater portion of mass from the shank is included in the collision. The higher

effective mass for the rigid ankle was evidenced by two mechanisms: firstly, effective mass as

calculated through the conservation of momentum was greater for the rigid ankle; secondly, the

sum of ball kinetic energy and elastic energy stored in the ankle at the end of contact were equal

between the rigid and non-rigid ankles, but, the reduction of foot velocity was smaller under the

rigid setting meaning a greater amount of energy was transferred from to ball but with a smaller

reduction in velocity. This indicates the effective mass was greater under the rigid setting,

supporting Kellis and Katis (2007) and Lees and Nolan (1998) who state the effective mass is

increased from a rigid foot and ankle. Shinkai, et al. (2013) found effective mass to also increase

with the physical mass of players, and therefore, effective mass is dependent on the physical mass

of the performer and the rigidity of the ankle during impact.

A less rigid ankle during kick impact results in a greater energy loss compared to a more

rigid ankle. During football kicking, energy can be lost in both the striking limb and the ball. For

our study ball position was held constant at impact start, and although small changes existed in

the relative foot-ball position as the ankle position changed during impact, it was assumed that

energy loss in the ball did not differ between the conditions. Under this assumption, the difference

in coefficient of restitution was solely due to the differing rigidity of the ankle joint. This lost

elastic energy was due to the ankle remaining in plantarflexion at the end of impact, 6.3 J of

energy were stored in the spring mechanism. Ball velocity between the two ankle configurations

would be equal if this stored energy was transferred into translational kinetic energy of the ball.

The translational kinetic energy of the ball was 76.7 J for the non-rigid ankle, and an increase of

6.3 J to 83.0 J is equivalent to a ball velocity of 19.1 m/s, comparable to that measured for the

rigid ankle (19.0 m/s).

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When all impact conditions were controlled for, increasing rigidity was beneficial to

impact efficiency, and therefore ball velocity. Previous analyses that did not identify an improved

efficiency with increased rigidity may have been confounded by other parameters. For example,

Ball, et al. (2010) suggested a number of impact characteristics such as ball orientation and impact

location that were not measured may also influence the impact phase. This highlights the benefits

of mechanical testing where all parameters could be controlled. To reduce the number of

parameters that can vary when testing with human performers, an intra-individual method could

be employed to reduce variation in parameters such as physical mass, strength and shoe type.

Experimental limitations did exist for the present study, because the mechanical limb did not

include soft tissue as present in the human body (muscle, tendon, ligament). This soft tissue may

influence the contribution of shank mass toward impact. While the simplification of the ankle and

foot structure within the present study has provided a strong theoretical background for the

application of kicking, future research is warranted with human participants to fully solve the

question about ankle rigidity and energy transfer. The practical applications of this work indicate

that strategies to reduce the magnitude of ankle plantarflexion during impact might increase ball

velocity. Effective strategies to reduce change in ankle plantarflexion and in-turn increase impact

efficiency might include controlling the impact location on the foot, to reduce the external torque

applied to the ankle, and increasing the muscle stiffness within the ankle joint, to increase the

internal torque applied to the ankle. Future work, however, is required to determine the

effectiveness of these strategies.

5.5. Conclusion

Two aims existed for the present study: to validate the ankle motion of a mechanical

kicking machine with a non-rigid ankle and to determine if differences exist between a rigid and

non-rigid ankle. The non-rigid ankle was in dorsiflexion for the first 31% of impact and moved

into plantarflexion for the remainder of the phase. Plantarflexion at impact end was 8.2 ± 0.7°.

This was a similar pattern and magnitude to both punt and instep kicking. Further, the contact

time was also comparable to human kicking, and the ankle motion of the mechanical kicking

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machine was therefore valid. Differences existed between the rigid and non-rigid ankle settings

for impact efficiency (foot-to-ball speed ratio). The higher impact efficiency was obtained by an

increase in effective mass and a reduction in energy losses. The greater effective mass for the

rigid ankle was quantified through the conservation of momentum and the energy transferred from

the foot to the ball. Rigidity of the ankle joint controls the contribution of mass from the shank

used in the collision. Energy losses were quantified from coefficient of restitution and the elastic

energy stored in the spring mechanism preventing plantarflexion. As the foot remained in

plantarflexion at the end of impact, energy stored in the joint was lost. Increasing ankle rigidity,

to decrease the forced plantarflexion, is beneficial for impact efficiency and therefore ball

velocity.


The aim of Chapter 5 was to identify if ankle plantarflexion during foot-ball impact

influenced impact efficiency. This research question contributed to aim 1 of the overall thesis.

This research question was answered used the mechanical kicking machine. It was identified

ankle plantarflexion was influential to impact efficiency. Further discussion of how to increase

impact efficiency can be found in section 10.2. Chapter 6 built upon this study by identifying

several strategies that players could use to reduce ankle plantarflexion, to in-turn increase impact

efficiency.

85

Chapter 6: Study 4 - Strategies to improve impact efficiency in

football kicking

This chapter has been published in the journal Sports Biomechanics and has undergone

the peer-review process.

Abstract: In football, kicking with high ball velocity can increase scoring

opportunities and reduce the likelihood of interception. Efficient energy transfer

from foot to ball during impact is important to attain a high ball velocity. It is

considered impact efficiency can be increased by reducing the change in ankle

plantarflexion during foot-ball impact. However, conflicting evidence exists,

questioning its effectiveness as a coaching cue. The aim of the present study was to

systematically analyse joint stiffness, foot velocity and impact location with a

mechanical kicking machine to determine if change in ankle plantarflexion during

foot-ball impact and ball velocity are influenced. Sagittal plane data of the shank,

foot and ball were measured using high-speed-video (4,000 Hz). Increasing joint

stiffness reduced change in ankle plantarflexion and increased ball velocity from a

greater effective mass. Increasing foot velocity increased change in ankle

plantarflexion and increased ball velocity. Distal impact locations increased change

in ankle plantarflexion and reduced ball velocity as coefficient of restitution

decreased. These results identify that change in ankle plantarflexion is a dependent

variable during foot-ball impact, and does not directly influence ball velocity.

Coaches can assess ankle motion during impact to provide feedback to athletes on

their impact efficiency.

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6.1. Introduction

Kicking is an important skill across the football codes, used to score goals and pass the

ball to fellow team members. By impacting the ball with their foot, a player imparts a combination

of flight characteristics that ultimately determines the outcome of the kick. Ball flight

characteristics include velocity, trajectory, and spin. While all flight characteristics must be

controlled for a kick to be successful, increasing ball velocity has many benefits during gameplay.

By kicking with a higher ball velocity, a player can increase the distance they can attempt to score

a goal thus increasing the number of scoring opportunities, and reduce the likelihood of

interception for the opposition by decreasing flight time. Therefore, technical strategies that

enhance ball velocity during kicking are important for performance.

Foot velocity has been identified as the most important technical component toward final

ball velocity. The relationship between foot and ball velocity has been identified through several

experimental designs: correlations within groups, comparisons of different players, comparisons

within players performing different tasks, and theoretical equations (Andersen, et al., 1999;

Nunome, et al., 2006a; Peacock, et al., 2017a; Shinkai, et al., 2013; Smith, et al., 2009).

Due to each players limitation in producing foot velocity, it is also important that players

impact the ball efficiently. Reducing the magnitude of change in foot and ankle position during

impact have been considered important factors toward impact efficiency (Asami & Nolte, 1983;

Ball, et al., 2010; Kellis & Katis, 2007; Lees & Nolan, 1998; Peacock, et al., 2017a; Sterzing, et

al., 2009). Despite what appears to be a clear relationship between foot and ankle motion during

impact with final ball velocity and a sound theory describing the mechanism, conflicting results

have also been identified. Nunome, et al. (2006b) identified a player within their analysed group

produced a large magnitude of change in ankle plantarflexion and a large magnitude of ball

velocity, and questioned the relationship between ankle motion with ball velocity. Shinkai, et al.

(2013) identified non-significant relationship between change in ankle plantarflexion and foot-

ball speed ratio in their analysis of 51 players performing the soccer instep kick.

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One key issue when analysing the influence of change in foot and ankle position during

impact with final ball velocity is the influence of confounding impact characteristics. While most

players experience forced, passive ankle plantarflexion during impact across kicking techniques

(Nunome, et al., 2006b; Peacock, et al., 2017a; Shinkai, et al., 2009), factors of foot velocity,

impact location and the position of the ankle at the beginning of impact have been suggested to

influence this motion (Peacock, et al., 2017a; Sterzing, et al., 2009). Theory indicates the resulting

ankle and foot motion during impact will be due to the sum of internal and external torques

applied. An external torque greater than the internal would result in plantarflexion, and vice-versa:

the external torque will be determined from the magnitude and point of application of the force

applied to the foot in relation to the ankle joint, and the internal torque will be determined from

the stiffness within the ankle. Further, due to the strong dependence of final ball velocity on initial

foot velocity (Andersen, et al., 1999), it is possible conflicting results between several studies

were caused from analysing the direct relationship between foot and ankle motion with final ball

velocity: greater ball velocities may have been achieved by greater foot velocities, and ankle

motion may have been influenced by foot velocity and impact location.

The aim of this study was to further explore ankle motion during foot-ball impact.

Conflicting results exist as to the importance of ankle motion toward final ball velocity, likely

due to confounding impact characteristics; therefore, a controlled methodology is needed to

appropriately identify its influence. The aim of this study was to systematically analyse three

characteristics and identify their relationship with change in ankle plantarflexion and ball

velocity: foot velocity, proximal-distal impact location on the foot, and joint stiffness under a non-

rigid ankle. Due to the difficulties with systematically analysing individual characteristics during

foot-ball impact with players (Peacock & Ball, 2016), a mechanical kicking machine designed to

replicate human ankle plantar/ dorsal flexion during impact performed kicks while each

characteristic was individually changed. This will provide useful information for future studies

analysing foot-ball impact and for coaches looking to improve an individual’s technique. It was

88

hypothesised that strategies which reduced the magnitude of ankle plantarflexion would increase

impact efficiency and/ or ball velocity.

6.2. Methods

6.2.1 Mechanical kicking machine

A mechanical kicking machine (Figure 6.1 (A)) performed punt kicks with an Australian

Rules Football ball (‘Match Ball’, Sherrin, Australia). The use of this limb allowed for a

systematic exploration of impact characteristics, an issue that has limited this research previously

and would be extremely difficult to perform with players. The key design feature of the limb for

the present study was controllable ankle stiffness; and the influence of impact location, foot

velocity, and ankle stiffness were systematically assessed. Because it is established the ankle is

forced into passive plantarflexion during impact (Shinkai, et al., 2009), the controllable ankle

stiffness was designed to prevent ankle plantarflexion. This was achieved via a spring mechanism:

synthetic rope, representing the tendon, connected to the dorsal aspect of the foot and passed

across the anterior aspect of the ankle joint (with a radius of 4 cm) before connecting to the shank

via a spring mechanism (Figure 6.1(B)). As the ankle underwent plantarflexion, the distance

between the origin and insertion of the synthetic rope increased and compressed the spring

mechanism. Ankle stiffness was controlled via two processes within the spring mechanism:

firstly, the initial compression of the spring could be altered, which increased the stiffness of the

ankle as indicated by Hook’s law; secondly, four different springs, each with different stiffness’

were used (50 N/mm, 86 N/mm, 174 N/mm, & 222 N/mm). The total length of each spring was

102 mm, and the initial compression could be set between the range of 1 to 27 mm. It was

identified the ankle motion produced by this limb validly replicated the human ankle during

impact, due to similarities with previous literature focusing on foot-ball impact (Peacock, et al.,

2017a; Shinkai, et al., 2009). This pilot testing was completed with a foot velocity of 16.5 m/s,

spring stiffness of 50 N/mm and initial spring deflection of 19 mm. Other key design features of

the limb included the segment lengths, masses and shape of the impacting surface to replicate that

of a typical Australian Football League player.

89

Figure 6.1: Mechanical kicking machine (A) and limb with rotation about the ankle (B).

Three impact characteristics were explored systematically for this study: foot velocity,

impact location and ankle plantarflexion stiffness. Foot velocity was altered by adjusting the

starting point of the limb over 11 positions as it began its forward swing while impact location

and ankle stiffness were held constant at 0.39 cm and 1118 N. Impact location was adjusted

through the platform supporting the ball over 11 positions; moving the height of this platform

changed the position of the ball relative to the foot, thus producing different impact locations

across the proximal-distal direction from the foot centre. No changes were made to the position

across the medial-lateral dimension, while foot velocity and ankle stiffness were held at 16.5 m/s

and 1118 N. Ankle stiffness was adjusted through the spring mechanism that prevented ankle

plantarflexion; twenty-four unique stiffness’ of the ankle were tested; the initial compression of

each spring was set at six positions between the range of 25 to 5 mm, increasing by 4 mm

increments. Impact location and foot velocity were held constant at 0.39 cm and 16.5 m/s.

6.2.2 Data collection and analysis

High-speed-video cameras recorded each trial at 4,000 Hz (Photron SA3, Photron Inc.,

USA). Markers were tracked in the sagittal plane to measure raw X-Y coordinates (ProAnalyst,

90

Xcitex Inc., USA). Data were smoothed using a low-pass Butterworth filter, with a cut-off

frequency of 170 Hz. The choice of cut-off frequency was based on five criteria: Fourier analysis,

previous literature (Nunome, et al., 2006b; Peacock, et al., 2017a), visual inspection of data

curves, and inspection of change in metric parameters.

Reflective tracking markers were attached to key landmarks of the foot and ball (Figure

6.2). Key anatomical landmarks were computed from the tracking markers using the procedure

of (Peacock, et al., 2017a). The foot centre was calculated from the midpoint between the foot top

and the foot bottom. The foot top was located at the approximate distal end of the tibia, and the

foot bottom was located at the approximate location of the third phalange, both on the dorsal

aspect of the limb. These two locations represented the most proximal and distal points on the

dorsal aspect of the foot, thus the foot centre position was the centre of the impacting surface on

the foot. Foot velocity was calculated from the first derivative of the foot centre over five frames

prior to impact. Ankle plantarflexion was calculated from markers attached to the shank, ankle

(axis of rotation), and the head of the fifth metatarsal, and the change in its position was calculated

from the initial and final positions at ball contact and release. Ball centre and orientation were

calculated from tracking markers attached to the ball and velocity was calculated from the first

derivative of positional data.

91

Figure 6.2: Reflective tracking markers and key anatomical landmarks.

A novel method was developed to calculate the impact location on the foot (Figure 6.3).

Previous methods to calculate the impact location in soccer kicking were not suitable due to the

unique ball shape (Ishii, et al., 2012). Because the radius of the Australian Football ball was not

constant due to its ellipsoidal shape, the intersecting point between foot and ball was dependent

on the orientation of the ball, the orientation of the foot, and the relative position of the two

objects. The dorsal aspect of the foot was modelled as a linear line (Equation 6.1), and this model

included information on the foot orientation and foot position in space. The ball shell was

modelled as an ellipse projected from its central position (Equation 6.2). The x and y coordinates

of the ball shell model were rotated to the orientation of the ball (Equation 6.3 and Equation 6.4).

The impact location of the foot was defined as the intersecting point between the two models (foot

and ball) at ball contact, and was represented as a vector in relation to the midpoint between the

top and bottom points of the foot. Positive values indicated a distal impact location from this

location.

92

𝐹𝑦 =

(𝐹𝐵𝑦 − 𝐹𝑇𝑦)

(𝐹𝐵𝑥 − 𝐹𝑇𝑥)∙ 𝐹𝑥 + (

(𝐹𝐵𝑦 − 𝐹𝑇𝑦)

(𝐹𝐵𝑥 − 𝐹𝑇𝑥)) ∙ −𝐹𝐵𝑥 + 𝐹𝐵𝑦 Equation 6.1

Where Fy = the position of the dorsal aspect of the foot, FBy = the y-coordinate of the

bottom of the dorsal aspect of foot, FTy = the y-coordinate of the top of the dorsal aspect of the

foot, FBx = the x-coordinate of the bottom of the dorsal aspect of foot, FTx = the x-coordinate of

the top of the dorsal aspect of foot, Fx = the x-coordinate of the dorsal aspect of the foot.

(

𝐵𝑆𝑥 − 𝐵𝐶𝑥

𝑅𝑥) + (

𝐵𝑆𝑦 − 𝐵𝐶𝑦

𝑅𝑦) = 1 Equation 6.2

Where BSx = position of the ball shell in the x-coordinate, BCx = position of the ball

centre in the x-coordinate, Rx = the short radius of the ball, BSy = position of the ball shell in the

y-coordinate, BCy = position of the ball centre in the y-coordinate, Ry = the long radius of the

ball.

𝐵𝑆𝑥,𝑅 = 𝐵𝑆𝑥 ∙ 𝑐𝑜𝑠𝜃 − 𝐵𝑆𝑦 ∙ 𝑠𝑖𝑛𝜃 Equation 6.3

Where BSx,R = x-coordinate of the rotated ball shell, θ = ball orientation.

𝐵𝑆𝑦,𝑅 = 𝐵𝑆𝑥 ∙ 𝑠𝑖𝑛𝜃 + 𝐵𝑆𝑦 ∙ 𝑐𝑜𝑠𝜃 Equation 6.4

Where BSy,R = y-coordinate of the rotated ball shell.

This method was limited because the foot and ball were assumed to be modelled by the

respective equations; the ball as an ellipse and the dorsal aspect of the foot as a linear line.

Inconsistencies in the true dorsal aspect of the foot from this linear line, in addition to the finite

sampling rate of the camera (4,000 Hz) meant there was not one finite impact location at visually

identified ball contact. Inspection of the model at ball contact identified either the foot and ball

were not in contact (Figure 6.3(A)) or the ball was partially deformed (Figure 6.3(B)). Therefore,

the impact location of the foot was defined by the point on the foot that produced the greatest

amount of ball deformation at visually identified ball contact. Ball contact was defined as the

93

largest distance between the ball surface and the perpendicular direction of the foot surface in the

direction of its path (the direction of ball deformation). One finite impact location on the foot

could be calculated with this definition. To validate this method, a correlation was between the

calculated foot impact location and the platform height. Impact location displayed a near perfect

linear relationship with platform height (R2 = 0.99; p < 0.001), and the developed method to

calculate impact location on the foot was therefore valid.

Figure 6.3: Video overlay of foot model (solid line) and ball model (dashed line) at ball

contact. Figure A identifies when the foot and ball models were not in contact at visually

identified ball contact, as depicted by the foot model being to the left of the ball model.

Image B identifies when the ball was partially deformed at ball contact, as depicted by the

foot model being to the right of the ball model.


To identify the relationship between each parameter pairing, linear, 2nd order, 3rd order

polynomials and power curves were fitted to the data. As there was no reason to expect a linear

relationship for each pairing, it was appropriate to expand the analysis to include other types of

curves if they fit the data more appropriately. The choice of most appropriate relationship was

based on five criteria (in no order): values of R2, p-value, visual inspection of data plots,

inspection of residual plots, and the statistical test from Hayes (1970). The statistical test from

Hayes (1970) was important to provide objectivity through this process.

94

6.3. Results

6.3.1 The influence of foot velocity

A third order relationship was identified between foot velocity and change in ankle

plantarflexion (Figure 6.4(A)). In the low range of foot velocity, change in ankle plantarflexion

increased exponentially. In the high range of foot velocity, change in ankle plantarflexion

decreased. Ball velocity increased linearly with foot velocity (Figure 6.4(B)).

Figure 6.4: The relationship between foot velocity and ankle plantarflexion (A); the

relationship between foot velocity and ball velocity (B). Impact location was held constant

at 0.4 cm and joint stiffness was held constant at 1118 N.

6.3.2 The influence of impact location

A second order relationship was identified between proximal-distal impact location and

change in ankle plantarflexion (Figure 6.5(A)). In the proximal impact locations, change in ankle

plantarflexion decreased when the impact location was moved toward the ankle. In the distal

impact locations, change in ankle plantarflexion plateaued. A negative, linear relationship was

identified between impact location and ball velocity (Figure 6.5(B)).

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Figure 6.5: The relationship between proximal-distal impact location and ankle

plantarflexion (B); the relationship between proximal-distal impact location and ball

velocity (B). Foot velocity was held constant at 16.5 m/s and joint stiffness was held

constant at 1118 N.

6.3.3 The influence of joint stiffness

A negative linear relationship was identified between change in ankle plantarflexion and

joint stiffness (Figure 6.6(A)). A positive linear relationship existed between ball velocity and

joint stiffness (Figure 6.6(B)).

Figure 6.6: The relationship between joint stiffness and ankle plantarflexion (A); the

relationship between joint stiffness and ball velocity (B). Impact location was held constant

at 0.4 cm and foot velocity was held constant at 16.5 m/s.

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6.4. Discussion and implications

6.4.1 The influence of foot velocity

Foot velocity influences change in ankle plantarflexion during impact. Change in ankle

plantarflexion increased with foot velocity due to the greater external torque applied about the

ankle. Change in ankle plantarflexion increased in the low range of foot velocity, indicating the

external torque increased with foot velocity. Change in ankle plantarflexion decreased in the high

range of foot velocity. This could indicate the external torque reduced, but, post-hoc analysis of

the ankle motion during impact (Figure 6.7) identified the ankle was dorsiflexing at the start of

impact for the higher range of foot velocity. Comparatively, the low range of foot velocities were

forced into plantarflexion immediately. This dorsiflexion motion at the start of impact combatted

against the forced plantarflexion, thus decreasing the overall magnitude. It was identified the

majority of elite and experienced players do dorsiflex at the start of impact for both instep and

drop punt kicking (Peacock, et al., 2017a; Shinkai, et al., 2009), and may have been an active

strategy used by the players.

Figure 6.7: Post-hoc analysis of ankle plantarflexion for two trials from the low (solid line)

and high (dashed line) foot velocities through impact. Each plotted line was comparable to

other trials in their respective groups.

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Dorsiflexing at the beginning of impact meant a linear relationship existed between foot

and ball velocity. Peacock and Ball (2017) found impact efficiency decreased with foot velocity

during their analysis with a mechanical kicking featuring a rigid ankle, a mechanical process of

the ball during impact. This suggested the relationship between foot and ball velocity was not

linear, but a power curve where the increase in ball velocity diminished. The authors compared

the non-linear and power curves, but revealed only a minimal difference where the linear curve

sufficed in explaining the relationship between foot and ball velocity. For the present study, it

was expected the power and linear curves to differ more notably because the non-rigid ankle

would also plantarflex with an increased foot velocity, further reducing impact efficiency.

However, this study again identified the linear relationship most appropriately described the

relationship between foot and ball velocity, but the dorsiflexing motion at the beginning of impact

possibly negated the potential reduction in ball velocity. As the foot was dorsiflexing, energy was

unable to be stored in the spring mechanism and was beneficial to ball velocity.

6.4.2 The influence of impact location

The proximal-distal impact location influences change in ankle plantarflexion during

impact. The external torque applied to the ankle decreased when impacting toward the ankle. For

the proximal impact locations, change in ankle plantarflexion increased as the impact location

moved distally along the foot. It was expected change in ankle plantarflexion to further increase

linearly throughout all impact locations due to the linear increase in torque associated with the

moment arm, however, there was only a minimal increase across the distal impact locations. Post-

hoc analysis of ankle motion during impact identified the distal impact location was forced into a

greater magnitude of plantarflexion earlier through impact, due to the higher external torque

applied to the ankle. In the final phase of impact, the ankle plantarflexion plateaued, and even

dorsiflexed a small magnitude in the most distal impact location (Figure 6.8). This ankle motion

at the end of impact has not previously been reported (Peacock, et al., 2017a; Shinkai, et al.,

2009), which represents a difference between the mechanical and human limbs. Inspection of the

video files identified in the distal impact locations the full range of motion within the ankle joint

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was reached, thus additional support to the spring mechanism was provided by the rigid structures

of the ankle joint. Further, some elastic energy of the spring mechanism was released in the most

distal impact location, evidenced by the dorsiflexion motion toward the end of impact. Regardless,

this difference had no effect on final ball velocity; inspection of the ball velocity profile during

impact identified ball velocity did not increase in the final phase of impact, similarly identified

by Peacock, et al. (2017a).

Figure 6.8: Post-hoc analysis of ankle plantarflexion for two trials from the proximal

(dashed line) and distal (solid line) impact locations. Each plotted line was comparable to

other trials in their respective groups.

Ball velocity was highest when impacting the ball closest to the ankle, meaning the

dorsiflexion at the end of impact did not improve performance. Peacock and Ball (2017) identified

ball velocity increased when the impact location on the foot was moved distally, because the

velocity of the impacting point on the foot increased as it moved further from the axis of rotation

(the knee). However, the ankle was rigid under their analysis, and thus a greater external torque

applied to the ankle did not force the ankle into plantarflexion. Impacting distally, which forces

the ankle into greater plantarflexion during impact, is detrimental to ball velocity. Post-hoc

analysis between impact location and coefficient of restitution, and between impact location and

effective mass identified significant linear relationships (p < 0.05). Coefficient of restitution

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decreased with distal impact locations, and effective mass increased with distal impact locations.

However, because it was identified the ankle reached its maximum range of motion prior to the

end of impact, foot velocity was subsequently increased in these trials and the calculations of

effective mass and coefficient of restitution were overstated. Distal impact locations increased

effective mass, however, this relationship was considered to be a result of reaching the full range

of motion. If the full range of motion was not met, effective mass would not have changed.

Coefficient of restitution decreased systematically with impact location in the distal direction,

despite the distal values being overstated due to reaching the full range of motion. This indicates

the negative effect of distal impact locations on coefficient of restitution should be larger in

magnitude. Most importantly, this identifies distal impact locations decrease coefficient of

restitution. Because the ankle is forced into greater magnitude with distal impact locations, more

energy is stored as elastic energy in the spring mechanism and is thus not returned to velocity in

either the foot or ball.

An optimal impact location on the foot is likely to exist. This study did not identify an

optimal impact location. However, it is expected ball velocity would decrease if the impact

location were continually moved proximally because the velocity of the impacting point decreases

as it moves closer to the axis of rotation (the knee). A limitation of the present study was the range

of impact locations analysed, it was not possible for any more impact locations in the proximal

direction to be analysed because the area covered by the deformed ball exceeded that of the 3d

printed shank and foot. Ishii, et al. (2012) identified an optimal impact location during their

analysis of the instep kick. They reported ball velocity to be highest at an impact location

approximately 1 cm distally toward the ankle from their defined foot centre of mass. Despite a

greater range of impact locations analysed by Ishii, et al. (2012) compared to the present study,

and a different method used to measure impact location from, a similar relationship appears to

exist with ball velocity on the distal side of the foot: ball velocity reduces as the impact location

moves distally from the approximate centre of mass.

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6.4.3 The influence of joint stiffness

The stiffness within the ankle joint influences change in ankle plantarflexion during

impact. In this analysis, increasing ankle joint stiffness via the spring mechanism increased the

internal torque applied by the ankle and reduced change in ankle plantarflexion during impact. In

human kicking, two strategies have been identified to increase the stiffness within the ankle joint:

increasing muscular strength and adopting a more plantarflexed position at the start of impact.

Ball, et al. (2010) identified junior players were forced into greater plantarflexion than seniors,

despite the lower force applied to the ball. The authors cautiously suggested the lower strength of

junior players may have caused the greater magnitude of plantarflexion, but, did indicate variation

in other impact characteristics such as ball orientation and impact location may have also

influenced the ankle motion between the groups. Adopting a more plantarflexed position at the

start of impact to increase ankle stiffness by relying on anatomical structures was identified by

both Sterzing, et al. (2009) and Peacock, et al. (2017a). By performing a qualitative analysis of

one individual within their group during soccer instep kicking, Sterzing, et al. (2009) suggested

the footwear designs such as the sole plate and heel counter may restrict a players’ ability to rely

on anatomical structures within the ankle and foot. Peacock, et al. (2017a) identified in Australian

football that players were able to significantly reduce the magnitude of change in ankle

plantarflexion during impact by adopting a more plantarflexed position at impact start, where

additional stiffness was provided by the hard-tissue structures at the end of the anatomical range

of motion. Coaches should employ each of these strategies to increase the stiffness within the

ankle joint of their players with a holistic approach. Firstly, assessing footwear designs to

determine how they limit the range of motion; secondly, testing the players’ ability to rely on

anatomical structures at the end of the ankle range of motion; thirdly, improving strength to

facilitate the ability to adopt a more plantarflexed position at the start of impact.

Increasing ankle joint stiffness increased ball velocity. This is the first study to provide

empirical evidence that increasing ankle stiffness under a non-rigid ankle was beneficial to ball

velocity. Several other studies have suggested increasing stiffness will translate to increased ball

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velocities (Ball, et al., 2010; Peacock, et al., 2017a; Sterzing, et al., 2009). Sterzing, et al. (2009)

performed an ANOVA analysis of ball velocity between five kicking conditions (3 shod, 1

barefoot, 1 sock) and identified a p-value of 0.05 at the group level. No post-hoc analyses were

performed between specific conditions, but visual inspection of the data revealed a trend toward

increased ball velocity in the barefoot and socked conditions over the shod conditions. Further,

this analysis may have been influenced by values of foot velocity. While observing differences in

change in ankle plantarflexion, suggested to be due to an increased joint stiffness, Peacock, et al.

(2017a) and Ball, et al. (2010) did not find statistically significant differences in foot-ball speed

ratio. The difference in foot-ball speed ratio identified by Ball, et al. (2010) between the junior

and senior groups was p = 0.02 with a medium effect, but was classified as non-significant due to

Bonferroni adjustment. However, foot-ball speed ratio may have also been influenced by different

body mass of the junior and senior groups, as identified by Shinkai, et al. (2013). The result of

this study identifies that increasing stiffness does increase ball velocity.

Increasing joint stiffness increased ball velocity through effective mass, as a greater

contribution of shank mass was included in the collision. Post-hoc analyses identified three trials

reached the full range of ankle motion (the three with the largest ankle plantarflexion), and were

removed from further post-hoc analysis. A positive significant linear relationship was identified

between joint stiffness and effective mass. Somewhat surprising, a negative significant linear

relationship was identified between joint stiffness and coefficient of restitution. This is in contrast

to Sterzing, et al. (2009), who stated increased rigidity may have increased energy dissipation

(coefficient of restitution). Further, it seems paradoxical that coefficient of restitution decreased

with an increased stiffness; under a constant force (due to constant foot velocity), it was expected

the magnitude of elastic energy stored in the spring mechanism to remain constant but with a

reduced magnitude of change in ankle plantarflexion. This relationship may have been influenced

by the four springs used (24 stiffness’ achieved from 4 springs at six initial deflections).

Additional analysis within each of the four springs identified a dissimilar pattern: coefficient of

restitution was not influenced by the initial deflection in three of the four springs, however,

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effective mass was influenced in all. Group comparisons of the springs also identified the two

springs with the greatest stiffness (174N/mm & 222 N/mm) produced significantly (p < 0.05)

lower coefficient of restitutions than the two springs with lowest stiffness (50 N/mm & 86 N/mm).

In the regression analysis of the entire group, this meant coefficient of restitution reduced with an

increasing stiffness due to the different springs and not the different levels of stiffness applied to

the ankle joint. Further work is required to explore the role of coefficient of restitution with joint

rigidity, but, it is clear that joint rigidity increases effective mass whereby a greater contribution

of shank mass is included in the collision.

6.4.4 Practical applications

Change in ankle plantarflexion during foot-ball impact does not directly influence impact

efficiency. This study identified how ball velocity and impact efficiency were influenced by three

impact characteristics: foot velocity, impact location and joint stiffness. Change in ankle

plantarflexion was a dependent variable under each of the analysed conditions. That is, change in

ankle plantarflexion is a consequence of other impact characteristics. This identifies that change

in ankle plantarflexion itself does not influence ball velocity and impact efficiency. Rather, other

characteristics, such as those systematically analysed in the present study, influence ball velocity

and impact efficiency. Practically, future researchers should not look at the relationship between

change in ankle plantarflexion with impact efficiency and ball velocity without taking into

account factors of foot velocity, impact location and others that relate to the internal and external

torque applied to the ankle joint. Future work should investigate how factors that influence the

internal and external torque applied to the ankle joint influence impact efficiency, such as impact

location which has received little-to-no attention with human kickers. It is also important to note

that this work was performed with a mechanical kicking machine, not human players. Differences

in energy transfer for human players might be expected due to the mechanical design, but, the

ankle motion was shown to be a valid representation of a human. Thus, the key theory of internal

vs. external torques discussed in this paper is valid.

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While it was just argued that change in ankle plantarflexion is not the independent

variable that influences impact efficiency, the results in this study identify that ball velocity and

impact efficiency were generally largest when change in ankle plantarflexion was minimised.

Practically, this means that coaches can analyse the foot and/ or ankle motion during impact to

provide useful feedback to athletes. With the development of camera technology, such as mobile

phone cameras capable of recording up to 960 Hz, the analysis of foot-ball impact is becoming a

possibility for everyday coaches. If a player produces a large magnitude of ankle plantarflexion,

the results within this study indicate impact efficiency and ball velocity can be increased by (1)

increasing the stiffness within the joint, and (2) by impacting the ball proximally toward the ankle.

However, it is not known what levels of change in ankle plantarflexion translate to the greatest

impact efficiency in human kickers. Additionally, coaches should also consider the distance and/

or speed that players are kicking, as a high foot velocity will induce a greater external torque

applied to the joint.

6.5. Conclusion

This study systematically analysed joint stiffness, foot velocity and impact location with

a mechanical kicking machine to determine their influence on change in ankle plantarflexion and

ball velocity. Increasing joint stiffness reduced change in ankle plantarflexion and increased ball

velocity. Increasing foot velocity increased change in ankle plantarflexion and ball velocity.

Impacting distally on the foot increased change in ankle plantarflexion and reduced ball velocity.

These results identify change in ankle plantarflexion was a dependent variable during foot-ball

impact, and did not directly influence impact efficiency. The practical outcomes of this work are

two-fold: (1) researchers should not assess the direct relationship between change in ankle

plantarflexion with impact efficiency or ball velocity without taking into account the impact

characteristics that influence the internal and external torque applied to the ankle, as change in

ankle plantarflexion, impact efficiency and ball velocity are dependent upon other impact

characteristics; (2) coaches can use ankle motion as a tool to assess the quality of impact, as

impact efficiency was generally largest when change in ankle plantarflexion was minimal.

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The aim of chapter 6 was to identify if several impact characteristics (foot velocity,

impact location, joint stiffness) influenced impact efficiency and/ or ball velocity, which

contributed to answering aim 1 of the overall thesis. This research question was answered by

performing a systematic exploration of foot-ball impact characteristics with the mechanical

kicking machine. Further discussion of how to increase impact efficiency can be found in section

10.2. The results from this chapter were also used to inform the task chosen to analyse in Chapters

7 and 8. Foot velocity was identified to influence ankle plantarflexion, and a constant task of a

30m kick was chosen to be examined for the intra-individual analysis.

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Chapter 7: Study 5 - Is there a sweet spot on the foot in

kicking?

This chapter has been published in Journal of Sports Sciences and has undergone the

peer-review process.

Abstract: In the collision between a striking implement and ball, the term “sweet

spot” represents the impact location producing best results. In football kicking, it is

not known if a sweet spot exists on the foot because no method to measure impact

location in three-dimensional space exists. Therefore, the aims were: (1) develop a

method to measure impact location on the foot in three-dimensional space; (2)

determine if players impacted the ball with a particular location; (3) determine the

relationship between impact location with kick performance; (4) discuss if a sweet

spot exists on the foot. An intra-individual analysis was performed on foot-ball

impact characteristics of ten players performing 30 Australian football drop punt

kicks toward a target. (1) A method to measure impact location was developed and

validated. (2) The impact locations were normally distributed, evidenced by non-

significant results of the Shapiro-Wilk test (p > 0.05) and inspection of histograms,

meaning players targeted a location on their foot. (3) Impact location influenced

foot-ball energy transfer, ball flight trajectory and ankle plantar/dorsal flexion. (4)

These results indicate a sweet spot exists on the foot for the Australian football drop

punt kick. In conclusion, the impact location is an important impact characteristic.

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7.1. Introduction

A successful outcome of any football kick is achieved by imparting a combination of

flight characteristics. Kicking is used by players in all football codes to score goals, gain ground

and/ or pass the ball to fellow team members. In Australian football drop punt kicking, because

the ball is in projectile motion after it is impacted by the foot, it will only reach a desired

destination if the necessary combination of flight characteristics is imparted onto the ball during

foot-ball contact. Within gameplay, it can be advantageous to impart a certain combination of

flight characteristics: increasing ball velocity while maintaining a low angle of elevation will

reduce the time the ball is moving between players, which, in-turn, can reduce the likelihood of

interception by the opposition; increasing ball velocity with a larger elevation angle can increase

the distance the ball travels before striking the ground, providing opportunities to shoot from

greater distances from the goal or clear the ball further down the ground when clearing the ball

from defence. Regardless of the techniques used within gameplay, all players reach their desired

target by applying a combination of flight characteristics by impacting the ball with their foot.

Researchers have identified biomechanical characteristics influential to flight

characteristics across kicking techniques. During the foot-ball impact phase, the key phase a

performer imparts ball flight characteristics during the kick, foot velocity, effective mass, and

ankle motion have been identified as important impact characteristics. Foot velocity has found to

be the most important factor for ball velocity (Asami & Nolte, 1983; Ball, 2008a, 2011; Kellis &

Katis, 2007; Lees, Asai, Andersen, Nunome, & Sterzing, 2010; Peacock & Ball, 2016, 2017), and

is a parameter that players can use to control kick distances (Peacock, et al., 2017a). The effective

mass of the striking limb, be it due to the physical mass of the performer (Shinkai, et al., 2013) or

the mass of the footwear used (Amos & Morag, 2002; Moschini & Smith, 2012; Sterzing &

Hennig, 2008), is also an important contributor toward ball velocity. However, the extent that

players can use this factor to increase ball velocity is limited: increasing the physical mass of the

shoe may translate to an increased effective mass, but, in-turn, foot velocity reduces where the

overall momentum of the limb remains constant (Amos & Morag, 2002; Moschini & Smith,

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2012). Recently, focus has been applied to the ankle motion and its role during impact. The ankle

has been found to be forced into passive plantarflexion during impact (Peacock, et al., 2017a;

Shinkai, et al., 2009), and minimising this motion has been identified beneficial to ball velocity

(Peacock & Ball, 2018a).

The impact location on the foot during kicking is emerging as an influential characteristic

to kick outcome, as identified by recent mechanical modelling studies. By analysing foot-ball

impact with a mechanical kicking machine, impact location across medial-lateral and proximal-

distal directions on the foot was shown to influence ball flight trajectory, ball velocity, ball spin

and ankle plantarflexion (Peacock & Ball, 2017, 2018b). For human kickers, impact location on

the foot is also emerging as influential to kick outcome. Mathematical modelling and finite

element analyses revealed impact location across either the proximal-distal or medial-lateral

directions of the foot was influential to ball velocity and ball spin (Asai, et al., 2002; Ishii, et al.,

2009, 2012).

The relationship between impact location and kick outcome measures with human kickers

has not been fully explored, and the analysis with the mechanical kicking machine indicates

further research is warranted. Currently, no method has been developed to measure impact

location across the medial-lateral and proximal-distal directions on the foot. A complex problem

exists when measuring the point of intersection between the foot and ball, due to non-uniform

changes in the foot surface relative to the segments centroid position. Furthermore, the difficulty

of measuring the point of intersection is again increased in kicking codes that use a non-spherical

ball, also due to the non-uniform location of the ball surface relative to the balls centroid position.

Thus, a method to calculate impact location must be developed to fully understand the influence

of impact location of human kickers.

Players anecdotally report there is a sweet spot on the foot, further suggesting impact

location influences kick outcome. The term “sweet spot” has traditionally been used by

researchers in the analysis of striking implements with a ball (rackets, bats) to represent the impact

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location that delivers maximum performance (Brody, 1981; Cross, 1998), and the term is also

used by players when assessing how they strike the ball. Specifically, if they struck the ball with

the desired location of their foot. Interestingly, the analysis of striking implements not only

revealed a sweet spot does exist, but the location of the sweet spot changes depending on how

performance is measured (Brody, 1981). For example, in an analysis of a cricket bat, Bower

(2012) found the ball speed sweet spot was distally toward the toe of the bat by 11 cm compared

to the apparent coefficient of restitution sweet spot.

The purpose of the present study was to determine the importance of impact location on

the foot. To explore this issue, the Australian football drop punt kick was analysed. Four specific

aims existed. Firstly, to develop a method to measure the impact location on the foot across both

dimensions that would present impact location as a distance from the foot centre across the

proximal-distal and medial-lateral impact locations. Secondly, to determine if players attempted

to strike the ball with a particular location on the foot. Thirdly, to identify the relationship between

impact location on energy transfer and ball flight trajectory, specifically foot-ball speed ratio,

coefficient of restitution, ankle plantar/dorsal flexion, effective mass and azimuth ball flight angle.

Fourthly, to discuss the concept of “sweet spot” in the application of football kicking using the

information gathered from the present analysis and discuss if a sweet spot exists on the foot.

7.2. Methods

7.2.1 Task, data collection and analysis

After gaining informed consent approved by the university human research ethics

committee, ten players between the age of 20 to 28 years old with various expertise playing

Australian Football (amateur through to elite competition) were recruited for the study (Table

7.1). Each player performed 30 drop punt kicks toward a target 30 meters in distance with a

standard Australian Football ball (Sherrin Match Ball; size = 5; mass = 0.455 kg; inflation = 69

kPa) in a laboratory setting that featured an athletics track surface. This kicking task simulated

kicking to a fellow team member on the field. The total number of kicks analysed varied between

each player due to the foot and/ or ball not remaining in the calibrated volume throughout the

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duration of foot-ball impact (Table 7.1). Despite this, a broad range of kick outcomes (i.e. kicks

that went to the left and right of the target, and hit the target) were captured, enabling an intra-

individual analysis to be performed.

Table 7.1: Characteristics of individual players.

Player Gender Height (m) Mass (kg) Shoe Number of

kicks analysed

1 Female 1.68 59 Training shoe 27

2 Male 1.78 87 Football boot 24

3 Male 1.85 87 Training shoe 25






9 Male 1.77 67 Indoor football boot 25

10 Female 1.57 55 Football boot 20

Three high-speed-video cameras were synchronised and positioned to record each

kicking trial (Photron SA3 & MC2, Photron Inc., USA). The measurement system was set up with

the Y-axis of the global coordinate system aligned from the kick location to the target, the X-axis

representing the medio/lateral dimension (right direction = positive), and the Z-axis in the vertical

dimension. The cameras were calibrated from a fixture consisting of 60 points (Xcitex Inc., USA),

yielding a root mean square error of < 1.0 mm within the measurement system (ProAnalyst

software, Xcitex Inc., USA).

A six degrees of freedom model comprising the shank, foot and ball was created for each

player. During a static trial, the distal, proximal and centroid positions of the shank and foot were

obtained from reflective markers attached to the lateral and medial epicondyles of the knee, the

lateral and medial ankle malleolus, and the head of the fifth (lateral aspect) and first (medial

aspect) metatarsals. Additional reflective markers were attached to the most dorsal aspect of the

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foot at the head of the metatarsals and at the malleolus to generate the surface location of the foot

relative to the foot segment for calculation of impact point (discussed below). The centroid

position and three radii of the ball (Figure 7.1b; rx, ry, rz) were determined from markers attached

at both ends of the long axis and two short axes. These key anatomical landmarks were projected

from tracking markers that remained on the players during the kicking trials. The shank and foot

were each represented by five spherical reflective markers 13 mm in diameter, fixed to the limb

using rigid strapping tape. Tracking markers on the ball consisted of flat rectangular pieces of

reflective tape (2.5 x 2.5 cm) with an 8mm black circular sticker attached to the middle. Spherical

markers could not be attached to the ball during kicking trials as their presence would impede the

player’s ability to hold the ball as it is dropped, possibly contact the ball during impact, and

influence ball flight.

Data of each kicking trial were measured at 4,000 Hz from 20 frames before to 20 frames

after visually identified ball contact and release, respectively. Markers were tracked in ProAnalyst

software (Xcitex Inc., USA) and three-dimensional X-Y-Z data of individual tracking markers

were imported into Visual3d software (C-Motion Inc., USA) where the six degrees of freedom

model was applied. Data were smoothed with a low pass Butterworth filter at a cut-off frequency

of 280 Hz. The choice of smoothing procedure was based on three criteria, comprising the results

from direct Fourier transform analysis (identifying the amplitude of the signal between 20 to 400

Hz), the cut-off frequencies used in previous studies examining foot-ball impact of kicking

(Nunome, et al., 2006; Peacock, et al., 2017), and visual inspection of the data curves at different

cut-offs.

Impact characteristics were calculated within Visual3d software. Initial and final

velocities of the foot and ball (individual axes & resultant) were calculated from the average

velocity of the segment centre of gravity over five frames before and after impact. Foot-ball speed

ratio was calculated from initial foot resultant velocity divided by final ball resultant velocity.

Effective mass was calculated from the change in ball momentum divided by the change in foot

velocity. Coefficient of restitution was calculated using the initial and final resultant velocities of

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the foot and ball. Change in ankle plantar/dorsal flexion angle was calculated from the six degrees

of freedom model (final angle subtract initial angle). Ball azimuth angle was calculated within

the global coordinate system over five frames after ball release (Peacock & Ball, 2017).

7.2.2 Calculation of impact point

A novel method was developed to calculate the impact location on the foot by modelling

the foot and ball as rigid bodies within Matlab software (R2016b, The Mathworks, Inc.). The

anterior surface foot was modelled as a semi-elliptical cylinder (Figure 7.1a; Equation 7.1-4) and

the ball an ellipsoid (Figure 7.1b; Equation 7.5). Both models were shells projected from their

centroid position based on their geometric properties derived during a static capture. The anterior

surface of the foot was constructed as a 200 x 200-point grid of X-Y-Z coordinates. Between each

kick there were two variables that distinguished the impact location; relative foot-ball orientation

and relative foot-ball displacement. Therefore, the grid was rotated and translated to the relative

orientation and position of the foot and ball. To identify the intersecting point on the foot and the

ball, each position of the grid was entered into the equation of the ball (Equation 7.5), which

solved the depth of the point relative to its shell. Any point on the shell yielded a value of 1, a

point that was in the shell yielded a value of < 1, and a point with a value > 1 was outside the

shell. The impact location on the foot was assumed to yield the smallest value from the entire

grid. From identifying the X-Y-Z coordinate of impact location, the impact location across the

medial-lateral and proximal-distal direction was calculated as the distance from the foot centre.

𝑥𝑙 =

𝑤𝑙

2cos ∅ Equation 7.1

Where xl = the x-coordinate of the foot grid for a given length of the foot; wl = the width

of the foot for a given length, calculated from Equation 2; θ = a vector comprising 200 linearly

spaced angles between 0° to 180°.

𝑤𝑙 =(𝑤𝑑 − 𝑤𝑝)

2 ∙ 𝑙∙ 𝑤𝑙 + 𝑤𝑝 Equation 7.2

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Where wd = the width of the foot at the distal end of the segment; wp = the width of the

foot at the proximal end of the segment; l = the length of the foot.

𝑦𝑙 = ℎ𝑙 sin ∅ Equation 7.3

Where yl = the y-coordinate of the foot grid for a given length of the foot; hl = the height

of the foot at a given length.

ℎ𝑙 =(ℎ𝑝 − ℎ𝑑)

𝑙∙ ℎ𝑙 + ℎ𝑑 Equation 7.4

Where hp = the height of the foot at the proximal end of the segment; hd = the height of

the foot at the distal end of the segment.

𝑥𝑙2

𝑟𝑥2

+𝑦𝑙

2

𝑟𝑦2

+𝑙2

𝑟𝑧2

= 𝑑 Equation 7.5

Where rx = the short radius of the ball; ry = the short radius of the ball (note: rx = ry); rz =

the long radius of the ball; d = the depth of the coordinate relative to the ball shell.

Figure 7.1: A) the grid representing the anterior aspect of the foot. B) the model of the ball

shell. Approximate locations of static markers are attached to the foot.


To determine if the method to calculate impact location on the foot was valid (aim 1),

criterion validation was performed. Criterion validation was performed across both dimensions

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of the foot (medial-lateral and proximal-distal) by calculating the standard error of estimate to

determine the level of error within the measurement in real-world units. The error was calculated

at the 95% confidence interval. Additional data were produced under a static condition using a

three-dimensionally printed foot with a boot attached for the validation. Under the static

condition, the position of the ball relative to the foot was moved systematically across each

dimension while ball orientation was held constant. The criterion measure was the distance

between the bottom edge of the ball to the centre of the foot, and the practical measure was the

calculated impact location for each dimension being assessed. A modified version of linear

regression was used to calculate the standard error of the estimate that included a coefficient for

the intercept but no coefficient for the slope. This was considered more appropriate than the

standard regression including also including a coefficient for the slope, because both measures

were in the same units (meters) but were offset by a constant distance because ball orientation

was held constant (the distance from the bottom point of the ball to the impact location).

To determine if players aimed to strike the ball with a particular location on their foot

(aim 2), the measured impact locations were tested for normality. The distribution of impact

location across for the proximal-distal and medial-lateral impact locations were tested for

normality both visually from histograms and through normality tests, using the Shapiro-Wilk test

(p > 0.05 indicating normality) within SPSS software, as recommended by Ghasemi and

Zahediasl (2012).

To determine the relationship between impact location with kick outcome measures (aim

3), bivariate regressions were performed. The two fundamental ball flight characteristics are ball

velocity and kick direction of travel: foot-ball speed ratio, coefficient of restitution, ankle

plantar/dorsal flexion, and effective mass have all been used to describe different factors

associated with energy transfer from foot to ball, and ball azimuth angle has been used to describe

the ball direction of travel; we determined the influence of impact location on these measures. To

achieve this, a bivariate regression analysis was performed within Matlab Software using the

Curve Fitting App. Linear and quadratic curves were assessed, and the type of relationship chosen

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was based on: inspection of the scatterplots, inspection of residuals, a theoretical underpinning,

and the significance test from Hayes (1970) to indicate if the second order regression significantly

improved the fit. Previously it was identified the proximal-distal dimension was mostly influential

to energy transfer, and the medial-lateral dimension was influential to ball azimuth (Peacock &

Ball, 2017), therefore, to reduce the analysis, each dimension of the foot was assessed using only

the respective performance measures.

The sweet spot location on the foot for each of the kicking measures were also identified

by interpreting the coefficients of the regression equations. The sweet spot is the impact location

that delivers maximum performance for the respective measure. Maximum performance for

azimuth ball flight angle was 0°, and we identified the impact location on the foot from the

regression equation that yielded a ball flight angle of 0° (Figure 7.3). For ankle plantar/dorsal

flexion during impact, because it has been established reducing ankle motion is beneficial to

performance, we set the sweet spot at a change in ankle angle of 0°, and identified the impact

location across the proximal-distal direction of the foot that corresponded to this point, as

indicated from the regression equation. Foot-ball speed ratio, coefficient of restitution and

effective mass are all scalar values, and increasing them is considered beneficial to performance

as they will all increase ball velocity. Therefore, the sweet spot location for these measures is

found at the highest point, which, can only be identified from the turning point in the quadratic

equation (see Figure 7.4 as an example). No turning point in the quadratic equations (the

maximum performance for the given measure) were identified in the range of data for some

individuals, therefore, no sweet spot was identified for that individual. Statistical confidence on

these locations were determined from 90% confidence intervals, calculated from the standard

error of the coefficients.

7.3. Results

7.3.1 Validation of impact location measurement

Criterion validation of the model identified the error to be less than the error within the

measurement system, and was therefore valid for use. The standard error across both dimensions

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of the foot was < 1 mm, and the 95% confidence interval was also < 1 mm. Therefore, the

methodology was appropriate to calculate impact location to the error within the measurement

system, 1 mm.

7.3.2 The distribution of impact locations between kicks.

All players produced a normal distribution of impact locations across both the medial-

lateral and proximal-distal directions of the foot, evidenced by the non-significant (p > 0.05)

results of the Shapiro-Wilk tests and visual inspection of the histograms. The mean impact

location across the medial-lateral direction was identified to be on the medial side of the foot for

all players, whereas the mean impact locations across the proximal-distal direction varied to be

either proximally or distally from the foot centre between players (Table 7.2; Figure 7.2 for Player

4).

Table 7.2: The mean and standard deviations of impact locations across the medial-lateral

and proximal-distal directions of the foot, measured from the foot centre. Positive values

represent the lateral and distal direction of the foot.

Player

Medial-lateral

impact location

(mm)

Proximal-distal

impact location

(mm)

1 -6 ± 3* 12 ± 22*

2 -8 ± 3* -29 ± 15*

3 -4 ± 3* 4 ± 14*

4 -7 ± 2* 11 ± 13*

5 -10 ± 2* 6 ± 18*

6 -10 ± 3* 24 ± 13*

7 -8 ± 3* 5 ± 22*

8 -2 ± 2* -1 ± 17*

9 -8 ± 3* 12 ± 16*

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10 -5 ± 3* -5 ± 24*

* indicates normally distributed, as quantified from the Shapiro-Wilk Test (p > 0.05).

Figure 7.2: The impact location for Player 4. A) Histogram of impact location across the

proximal-distal impact location (cm from foot centre of mass). B) Histogram of impact

location across the medial-lateral impact location (cm from foot centre of mass). The

bivariate distribution plot has been superimposed onto the foot, and the scale (C)

represents the relative distribution.

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7.3.3 The relationship between impact location and kick outcome.

A positive linear relationship existed for nine players between medial-lateral impact

location with ball azimuth flight angle. The sweet spot, the impact location that delivered an

azimuth ball flight of 0°, occurred on the medial aspect of the foot for all players (Table 7.3;

Figure 7.3 for Player 8). The direction of the relationship meant that impact locations to the lateral

side of this sweet spot resulted in an azimuth ball flight in the lateral direction.

Table 7.3: Relationship between medial-lateral impact location and azimuth ball flight

angle.

Player

Linear Second order Sweet

spot

location R-squared Classification R-squared Classification

1 0.47^ Large 0.59^* Nearly Perfect -6 ± 1

2 0.58^ Nearly Perfect 0.58^ Nearly Perfect -7 ± < 0.1

3 0.34^ Large 0.35^ Large -4 ± 1

4 0.52^ Nearly Perfect 0.53^ Nearly Perfect -7 ± 1

5 0.40^ Large 0.40^ Large -12 ± 1

6 0.39^ Large 0.39^ Large -12 ± 1

7 0.08 Small 0.10 Medium -8 ± 2

8 0.45^ Large 0.45^ Large -2 ± < 0.1

9 0.27^ Large 0.27^ Large -10 ± 2

10 0.20^ Medium 0.30^ Large -3 ± 1

^ indicates p < 0.05; * indicates significance from Hayes (1970); bolded relationship

represents chosen relationship.

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Figure 7.3: The relationship between medial-lateral impact location and azimuth ball

flight angle for Player 8. The sweet spot location (the point on the horizontal axis) can be

identified by identifying the azimuth ball flight angle (vertical axis at 0°) from the

regression line. Positive values represent the lateral direction from foot centre (impact

location) and ball flight trajectory (azimuth ball flight angle).

Figure 7.4: The proximal-distal (P-D) sweet spot locations for Player 4, as identified by the

quadratic regressions between impact location with foot-ball speed ratio (FB Ratio),

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coefficient of restitution (COR), and effective mass (EM). Positive values of impact

location represent the distal location from the foot centre.

A positive linear relationship was identified in all players between proximal-distal impact

location with ankle plantar/dorsal flexion (Table 7.4). The sweet spot, the location that produced

a change in ankle angle of 0°, varied between players to occur on either proximally or distally

from the foot centre. As players impacted the ball at a location distally from the sweet spot, the

magnitude of plantarflexion increased.

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Table 7.4: Relationship between proximal-distal impact location and change in ankle

plantar/dorsal flexion.

Player


spot


1 0.94^ Perfect 0.94^ Perfect -12 ± 3

2 0.89^ Perfect 0.89^ Perfect -18 ± 2

3 0.81^ Perfect 0.82^ Perfect -4 ± 3

4 0.73^ Nearly Perfect 0.78^* Nearly Perfect 9 ± 2

5 0.84^ Perfect 0.84^ Perfect -11 ± 4

6 0.64^ Nearly Perfect 0.71^* Nearly Perfect 8 ± 5

7 0.93^ Perfect 0.93^ Perfect 1 ± 2

8 0.93^ Perfect 0.94^* Perfect 9 ± 1

9 0.88^ Perfect 0.89^ Perfect 5 ± 2

10 0.87^ Perfect 0.87^ Perfect -27 ± 5



Quadratic relationships between proximal-distal impact location and foot-ball speed ratio

and a sweet spot location were identified in four players (Table 7.5; Figure 7.4 for Player 4).

When players impacted the ball either side from the sweet spot location, foot-ball speed ratio

decreased. Negative linear relationships were identified between proximal-distal impact location

and foot-ball speed ratio in Player 2 and Player 7. A positive linear relationship existed between

proximal-distal impact location and foot-ball speed ratio for Player 3.

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Table 7.5: Relationship between proximal-distal impact location and foot-ball speed ratio.

Player


spot


1 <0.01 Trivial <0.01 Trivial -

2 0.11 Medium 0.11 Medium -

3 0.10 Medium 0.10 Medium -

4 0.33^ Large 0.53^* Nearly Perfect 4 ± 7

5 0.01 Trivial 0.08 Small -

6 <0.01 Trivial 0.04 Small -

7 0.23^ Medium 0.26^ Large -

8 0.01 Small 0.31^* Large -2 ± 6

9 <0.01 Trivial 0.34^* Large 7 ± 6




Five players displayed a linear relationship between proximal-distal impact location and

effective mass that was negative in direction for all (Table 7.6). Three players displayed a

quadratic relationship, and a sweet spot could be identified in each (Figure 7.4 for Player 4).

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Table 7.6: Relationship between proximal-distal impact location and effective mass.

Player


spot


1 0.11 Small 0.28^* Small 3 ± 6

2 0.20^ Medium 0.20 Medium -

3 < 0.01 Trivial < 0.01 Trivial -


5 0.61^ Nearly Perfect 0.63^ Nearly Perfect -

6 0.09 Small 0.12 Medium -



9 0.17 Medium 0.23^* Medium 3 ± 12

10 0.54 Nearly Perfect^ 0.60^ Nearly Perfect -



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Quadratic relationships and a sweet spot location were identified between proximal-distal

impact location with coefficient of restitution for five players (Table 7.7; Figure 7.4 for Player 4).

A positive linear relationship was in one player, Player 5.

Table 7.7: The relationship between proximal-distal impact location and coefficient of

restitution.

Player


spot


1 0.02 Small 0.02 Small -


3 0.03 Small 0.15* Medium -4 ± 3

4 0.20^ Medium 0.37^* Large 9 ± 2

5 0.15^ Medium 0.17 Medium -


7 0.05 Small 0.08 Small -

8 0.08 Small 0.41^* Large 9 ± 1

9 0.11 Medium 0.35^* Large 5 ± 2

10 <0.01 Trivial 0.30^* Large -27 ± 5



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7.4. Discussion

The aim of the present study was to determine the influence of impact location on kick

outcome by quantitatively answering three aims: (1) by developing and validating a method to

calculate impact location across both the medial-lateral and proximal-distal dimensions of the

foot; (2) by determining if players aimed to strike the ball with a particular location on their foot;

and (3), by identifying the relationship between impact location with kick outcome measures, and

interpreting the regression equations to identify if there was an impact location that delivered the

greatest performance. From an analysis of the Australian football drop punt kick, the key results

of this study were: (1) the developed method to calculate impact location was valid; (2) the

measured impact locations were normally distributed; and (3) the impact location across the

medial-lateral and proximal-distal directions of the foot influenced kick outcome, and, an impact

location that produced the highest performance was identified for some individuals.

7.4.1 Did players target a specific location on their foot?

In the present analysis of the Australian football drop punt kick, all players produced a

normal distribution of impact locations across both dimensions of the foot, indicating they

targeted a specific location. Because none of the players were novices, but had kicking experience,

the targeted impact location was best for the task. End-point variability did exist within this

distribution, but its influence was random, where the mean impact location was located at, or

close to, the true sweet spot. Players impacted the ball with a precise location on their foot.

7.4.2 Medial-lateral impact location

The medial-lateral impact location influenced azimuth ball flight angle. Nine of ten

players produced a linear relationship between medial-lateral impact location with azimuth ball

flight angle (Table 7.3), supporting the findings of Peacock and Ball (2017) who also identified

this pattern in their analysis with a mechanical kicking machine analysing the drop punt kick. As

discussed by Peacock and Ball (2017), the oblique impact theory indicates the angle of the

intersecting surfaces influences the angle of trajectory. Across the medial-lateral dimension of the

foot, the surface angle of the foot changes substantially, where azimuth ball flight trajectory will

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be 0° at the impact location where the medial-lateral surface angle is perpendicular to the direction

of the target. For all players, this location was on the medial aspect of the foot due to its

asymmetrical shape, as found by Peacock and Ball (2017) on their mechanical kicking machine.

Because the surface angle of the foot changes substantially across the medial-lateral dimension,

the impact location across the medial-lateral direction on the foot is a key variable toward azimuth

ball flight angle.

7.4.3 Proximal-distal impact location

The proximal-distal impact location influenced ankle plantar/dorsal flexion during foot-

ball impact (Table 7.4). A linear relationship was identified for all players between impact

location with ankle plantar/dorsal flexion, where impacting the ball distally from this location

corresponded to an increased ankle plantarflexion. Because ankle motion during foot-ball impact

is passive (Nunome, et al., 2006b; Peacock & Ball, 2018a, 2018b; Shinkai, et al., 2009), the

resulting ankle motion is largely dependent upon the torque applied to the ankle joint. Between

kicks in the present study, the average force applied to the foot changed minimally because the

kick distance was constant (impact force associated with kick distance; (Peacock, et al., 2017a)).

Therefore, the resulting torque applied about the ankle was mostly dependent upon the moment

arm, which is the distance between the proximal-distal impact location and the ankle joint. Thus,

the proximal-distal impact location is an influential characteristic to ankle plantar/dorsal flexion

during impact, in addition to the starting angle of the ankle (Peacock, et al., 2017a) and the

stiffness of the ankle joint (Ball, et al., 2010; Peacock & Ball, 2018b).

Impact location influenced foot-ball speed ratio in most players and a location that

produced the greatest impact efficiency was identified in four players (Table 7.5). Foot-ball speed

ratio has been used previously to describe the efficiency of energy transferred from foot to ball

(Ball, et al., 2010; Peacock, et al., 2017a; Shinkai, et al., 2013; Smith, et al., 2009), and we

identified in players an impact location that produced the highest impact efficiency, as quantified

by foot-ball speed ratio. Further, we identified three players produced linear relationship with

foot-ball speed ratio, meaning impact efficiency was influenced by the impact location in these

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players as well. These results suggest the impact location across the proximal-distal direction was

influential to energy transfer.

While an impact location yielding the highest efficiency was not identified across all

players, it is hypothesised an optimal relationship does exist but the range of impact locations

measured was not large enough. Because we analysed drop punt kicking, where the ball is dropped

prior to being impacted by the ball, it was not possible to systematically control impact location.

The range of impact location in the present study ~70 mm, far less than the overall length of the

foot. Furthermore, foot-ball angle is another variable that could not be controlled due to the ball

drop. For a given impact location, the resulting area covering the foot due to deformation is also

dependent upon the relative foot-ball orientation. Foot-ball angle has also been identified to

influence ball velocity (Peacock & Ball, 2017). The variation in foot-ball angle will add noise to

the relationship between impact location with kick outcome measures (not just impact efficiency).

It is hypothesised a quadratic relationship will exist in all players between impact location with

impact efficiency. As players impact distally on the foot, the ankle and foot are forced into

plantarflexion which reduces impact efficiency. Impacting proximally produces a lower velocity

of the impacting point compared to a more distal location, which Peacock and Ball (2017)

identified was detrimental to ball velocity. Supporting this hypothesis, Ishii, et al. (2012)

identified a quadratic equation to impact location and standardised ball speeds in all five of their

tested players performing the soccer instep kick. Because the authors were analysing the soccer

instep kick where the ball is stationary prior to being impact, the impact location could be and

was controlled by altering the height of the ball above the ground with a tee; the total range of

tested impact locations was 140 mm across the proximal-distal direction.

It could not be clearly identified how impact location influenced impact efficiency in

human kickers. In the present analysis, coefficient of restitution and effective mass were both

associated with proximal-distal impact location between players (Table 7.6 and 7.7). In their

analysis with a mechanical kicking machine, Peacock and Ball (2018b) found distal impact

locations decreased ball velocity. This decrease in ball velocity was due to decreases in coefficient

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of restitution as the greater magnitude of ankle plantarflexion at the end of impact with distal

impact locations meant more elastic energy was stored in the spring mechanism (that represented

the muscle tendon unit) and was not transferred to ball velocity. Conversely, increases to joint

stiffness, which also decreased ankle plantarflexion and increased ball velocity, increased

effective mass and had no effect on coefficient of restitution as less of the kinetic energy from the

shank could be transferred to the ball via the ankle joint. This mechanical modelling suggested

different strategies to reduce ankle plantarflexion influenced impact efficiency through different

mechanisms. Specifically, proximal impact locations influence impact efficiency through

coefficient of restitution and not effective mass. In this analysis with human kickers, however, it

could not be clearly seen that impact location influenced coefficient of restitution and not effective

mass, as identified in the mechanical kicking machine.

The difference between impact location influencing energy transfer mechanisms for the

human kicking and the mechanical kicking machine might be explained by two reasons. Firstly,

variance in other impact characteristics, such as foot-ball angle, might influence individual energy

transfer mechanisms and confound each individual relationship by adding random noise (as

discussed previously with foot-ball speed ratio). Secondly, the observed difference might be due

to differences in design between the mechanical kicking machine and the human ankle. During

ankle plantarflexion of the kicking machine, all energy had to be stored in the spring mechanism.

This storage of elastic energy during ankle plantarflexion can occur with stretching of the muscle

tendon unit for the human ankle. But, plantarflexion of the human ankle can also occur from an

increase in length of the muscle component within the muscle tendon unit. Furthermore, the

lengthening of the muscle component is more likely to occur as impact location moves distally.

This is due to the increased moment arm with distal impact locations that requires an increased

internal muscle force to maintain an isometric contraction – which is possibly exceeded at distal

impact locations. As the muscle tendon unit increases length – not from stretching where the

elastic energy would be stored but during an eccentric muscle contraction – the shank’s ability to

contribute kinetic energy to the collision is impaired because of the diminished force cannot be

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transferred through the muscle tendon unit to maintain rigidity. Thus, the decreased effective mass

is due to less of the shank mass (or, the kinetic energy) included in the collision.

Important to note, muscle activation of the ankle dorsal flexors still appears to be

important toward producing high impact efficiency and ball velocity. Because the muscles can

act as a brake during muscle lengthening (Dickinson, et al., 2000; Williams, Regnier, & Daniel,

2012), the foot does not rotate freely around the bottom of the shank. This introduces some

component of the shank toward the collision. Therefore, while no studied has determined the

efficaciousness, these results support previous suggestions that players could perform strength

training of the ankle musculature to improve impact efficiency (Ball, et al., 2010; Peacock & Ball,

2018a, 2018b).

7.4.4 Is there a sweet spot on the foot?

The sweet spot is a term classically used in the analysis of striking implements for the

impact location that produces the best results for the outcome of the task. We argue two key points

that support a sweet spot exists on the foot during Australian football drop punt kicking. Firstly,

all players produced a normal distribution of impact locations, meaning, they specifically targeted

a location on their foot. There was a distribution of impact locations, but this distribution was

random due to end-point variability. Secondly; the impact location influences the outcome of the

task. The medial-lateral direction influences azimuth ball flight trajectory, and the proximal-distal

direction influences ankle motion and energy transfer. Depending on the desired flight

characteristics imparted onto the ball, players should look to impact the ball with the

corresponding impact location on the foot that would yield those flight characteristics. Across the

medial-lateral dimension for the present study, as an example, the sweet spot location was

identified to be on the medial aspect of the foot as it the task required players to kick straight

toward the target. While not directly associated with ball flight, but an important characteristic

nonetheless, is the influence of impact location on ankle plantar/dorsal flexion. Impacting the ball

on the foot with a distal impact location will force the ankle into a large magnitude of ankle

plantarflexion, which will put the player at a greater risk of injury (Tol, et al., 2002) and produce

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pain within the ankle and metatarsophalangeal joint. From these two points, we conclude that a

sweet spot does exist on the foot. But, it is important to mention, the location of the sweet spot is

likely to change depending on the task and how performance is measured. Future research could

explore how players functionally adapt their impact characteristics to satisfy different task

constraints.

7.5. Conclusion

The present study identified the importance of impact location on the foot to the outcome

of the Australian football drop punt kick by quantitatively answering the following three aims:

(1) a method to calculate the impact location across the medial-lateral and proximal-distal

dimensions of the foot was developed and validated to the accuracy of the measurement system

(< 1.0 mm); (2) it was identified that players impacted the ball with a specific location on their

foot, evidenced by normal distributions of the impact location across both dimensions of the foot;

and (3) impact location influenced kick outcome measures (energy transfer, ball flight trajectory,

ankle motion), and the location producing the best results (sweet spot) for several measures was

identified. From these results, we conclude there is a sweet spot on the foot during the Australian

football drop punt kick.


Impact location on the foot was identified in previous chapters (Chapter 4 and 6) to

influence impact efficiency, ankle plantarflexion and ball flight characteristics (aims 1 and 2 of

the present thesis). The aim of the present Chapter was to again determine the effect of impact

location on impact efficiency, ankle plantarflexion and ball flight characteristics, but analysing

human kickers instead of using the mechanical kicking machine. The results from the present

chapter support the findings from previous work and contribute to answering aims 1 and 2 of the

overall thesis. A further discussion of how proximal-distal impact location influences impact

efficiency and ankle plantarflexion is found in section 10.1.3. A discussion of how medial-lateral

impact location influenced ball flight characteristics is found in section 10.2.1.

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Chapter 8: Study 6 - Kick impact characteristics of accurate

football kicking

This chapter has been published in the journal Human Movement Science and has

undergone the peer-review process.

Abstract: Accurate kicking is essential to team success in Australian football. It is

not known how foot-ball impact characteristics influence kicking accuracy, nor is it

known if variability in foot-ball impact characteristics is functional or dysfunctional

to performance. The aim of this study was to identify the relationship between foot-

ball impact characteristics and kicking accuracy and determine if variability in foot-

ball impact characteristics influenced performance variability. Ten players

performed 30 drop punt kicks toward a target with an Australian football ball.

Kicking accuracy (measured as the horizontal distance from the target in the

perpendicular direction of the kick), initial ball flight characteristics, and foot-ball

impact characteristics, including a novel method to calculate impact location on the

ball, were measured. Variability was indicated using standard deviation of foot-ball

impact and ball flight characteristics. Multiple linear regression analysis identified

azimuth ball flight trajectory as the most important ball flight characteristic

influencing kicking accuracy, not ball flight characteristics associated with ball

curve. Intra-individual multiple linear regressions identified azimuth ball impact

location and foot-ball angle were the two most important factors explaining variance

in azimuth ball flight trajectory, the chosen performance measure. Variability existed

between and within players. Reduced variability in azimuth ball flight trajectory, the

chosen performance measure, was associated with reduced variability in foot-ball

impact characteristics. This result indicated variability in foot-ball impact

characteristics was dysfunctional for performance in the analysed task. Foot-ball

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impact characteristics and variability in foot-ball impact characteristics influences

accuracy of Australian football drop punt kicking.

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8.1. Introduction

Kicking is an important skill across the football codes. Under certain gameplay situations,

the demand of accuracy for kicking is high. In Australian football, kicking with high accuracy is

required to successfully score goals, to pass to team members, and to clear the ball when relieving

defensive pressure. The drop punt kick is the most common kicking style in Australian football.

The drop punt kick is characterised by the player releasing the ball from his/ her hands, forcefully

impacting the ellipsoidal ball with the long axes of the foot and ball aligned, and imparting a

distinct back-spin for ball flight. Because the ball is in projectile motion after it leaves the foot,

accurate kicking is achieved by imparting an appropriate combination of flight characteristics

required to reach the target.

Research exploring the foot-to-ball impact phase (hereafter referred to foot-ball impact)

of Australian football drop punt kicking has focused almost entirely upon the production of ball

speed. It is clear that foot speed immediately prior to impact is the most important contributor

toward ball speed (Ball, 2008a, 2011; Ball, et al., 2010; Peacock & Ball, 2017) and is a strategy

used by players to alter kick distances (Peacock, et al., 2017a). Despite the large contribution of

foot speed to ball speed, players must still control other ball flight characteristics to ensure

adequate energy transfer from foot to ball. Recent analyses with a mechanical kicking machine

have identified ball orientation and impact location at the beginning of impact and ankle stiffness

throughout impact influence ball speed (Peacock & Ball, 2017, 2018a, 2018b).

How players configure their foot-ball impact characteristics to attain accurate kicking is

almost entirely unexplored. Research has identified how individual impact characteristics

influence individual ball flight characteristics across different football kicking codes. However,

given the importance of kicking accuracy required for goal scoring, passing and overall team

success, further work is required to provide the link between these impact characteristics with a

measurement of kicking accuracy. In the Australian football drop punt kick, impact location, ball

orientation and foot speed were influential to ball flight characteristics of back-spin rate and

azimuth ball flight trajectory in an analysis with a mechanical kicking machine (Peacock & Ball,

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2017). In the soccer instep kick, a trade-off between impact location and ball speed and ball spin

has been identified (Asai, et al., 2002; Ishii, et al., 2009). These studies indicate the importance

of foot-ball impact characteristics toward individual ball flight characteristics, and work is

required to provide the link between impact and kicking accuracy.

While identification of the direct mechanisms associated with accurate football kicking

is important, understanding how a player varies their technique over several repetitions can also

help explain kicking accuracy. The ultimate measure of performance for accurate kicking is the

final position of the ball relative to the desired target. In gameplay of Australian football, an

attempt at goal is only successful when the final position of the ball travels within the goal posts.

Performance variability is the distribution of the final position over several repetitions, and can

be easily identified in gameplay by attempts at goal that were either successful or unsuccessful.

Arguably of more importance to human movement scientists is the variability in the movement

pattern that produces the outcome of the task (Bartlett, Wheat, & Robins, 2007). Somewhat

surprisingly, it has been identified that better skilled players, those that produce less performance

variability (i.e. more consistent, successful accurate outcomes), produce more movement

variability in the proximal segments than the less skilled counterparts (Arutyunyan, Gurfinkel, &

Mirskii, 1968; Robins, Davids, Bartlett, & Wheat, 2008). Thus, to achieve accurate end-point

positions, skilled players do not consistently produce an ‘ideal’ or ‘optimal’ technique (Glazier,

Reid, & Ball, 2015). In the context of football kicking, some researchers have sought to identify

if better skilled football players utilise increased or decreased variability in the approach and

swing phases of various football kicking techniques (Ford & Sayers, 2015; Morris, Sayers, &

Stuelcken, 2016; Sayers & Morris, 2012). It has been argued that increased variability can be

functionally used by players to adapt to different gameplay conditions incurred from fatigue,

surface conditions and playing environment (Ford & Sayers, 2015). Thus, increased variability

can be either functional or dysfunctional, depending on the event or phase of analysis throughout

the kicking execution (i.e. proximal segments, end-point position or performance outcome).

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It is not known if accurate drop punt kicking is achieved through increased or decreased

variability at foot-ball impact, nor has this been assessed in any football kicking technique. The

analysis of impact characteristics during the golf drive identified better skilled players reduced

variability in impact characteristics (Betzler, Monk, Wallace, & Otto, 2012, 2014). This finding

is relevant for football kicking, as golf and football kicking both accelerate the ball via a collision.

However, the ball shape distinctly differs between the tasks, with an ellipsoidal shape used in

Australian football and spherical ball in golf. This unique ball shape of Australian football may

lead to degeneracy at foot-ball impact of the drop punt kick. Peacock and Ball (2017) identified

individual impact characteristics (impact location, ball orientation, etc.) influenced several ball

flight characteristics. Players could therefore use multiple combinations of impact characteristics

to achieve similar ball flight characteristics and accurate kick outcomes. Skilled players might

utilise this redundancy to remove any errors in technique introduced during the leg swing of the

kicking skill by functionally varying foot-ball impact characteristics. Thus, when performing the

Australian football drop punt kick, there are two distinctly different strategies that a player might

be able to use to produce accurate football kicking, (1) reducing the magnitude of variability in

foot-ball impact characteristics or (2) functionally increasing variability in foot-ball impact to

mitigate errors incurred during the forward swing and ball drop.

The aim of the present study was to identify how foot-ball impact characteristics influence

kicking accuracy in the Australian football drop punt kick. Accurate drop punt kicking in

Australian football is important to overall team success, as it is the main technical skill used for

scoring and passing moderate and long distances. The link between foot-ball impact

characteristics with kicking accuracy has not been established, nor is it understood how accuracy

is influenced by movement variability at foot-ball impact. Thus, to further understand how

accurate kicking is obtained, the first aim of the study was to identify the relationship between

foot-ball impact and kicking accuracy by (1A) identifying the relationship between ball flight

characteristics and kick accuracy and (1B) identifying the relationship between foot-ball impact

and ball flight characteristics. This process of working backwards from the outcome

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systematically allowed the direct mechanisms to be identified. The second aim of the study was

to identify if performance variability was associated with increased or decreased levels of

variability in foot-ball impact characteristics.

8.2. Methods

8.2.1 Task, data collection and analysis

After signing informed consent forms approved by the university’s human research ethics

committee, ten players of various experience (2 – 15 years playing competitively) kicked a

standard Australian football (Sherrin Match Ball; inflation = 69 kPa) from a defined kicking area

toward a player 30 meters in distance. Each player performed this kick 30 times. The player

catching the ball was instructed to move across the 30-meter line perpendicular to the kick

direction and catch the ball. This task simulated a common pass performed in gameplay of

Australian football. Accuracy was defined as the horizontal displacement between the constant

central position and the catch position in the perpendicular direction of the kick. Kicking accuracy

was measured by a two-dimensional video camera (50 Hz) and digitised using ProAnalyst

software (Xcitex Inc., USA). Values were calculated as a directional vector (positive values

represented kicks that were caught on the lateral side of the kicking limb).

Three-dimensional foot-ball impact and initial ball flight characteristics were measured

at 4,000 Hz for each kick. Three high-speed video cameras (Photron SA3 & MC2, Photron Inc.,

USA) were synchronised and positioned to record reflective markers attached to the lateral aspect

of the shank, foot and ball from 20 frames before to 20 frames after foot-ball contact. The Photron

SA3 camera was positioned perpendicular to the direction of the kick, and two Photron MC2

cameras were positioned at an offset angle of approximately 40°. The shank and foot were each

represented by five spherical reflective markers 13 mm in diameter, fixed to the limb using rigid

strapping tape. Five tracking markers on the ball consisted of flat rectangular pieces of reflective

tape (2.5 x 2.5 cm) with an 8mm black circular sticker attached to the middle. Markers were

tracked in ProAnalyst software to produce three-dimensional X-Y-Z data. The system was

calibrated using the right-hand rule, with the Y-axis pointing toward the target, Z-axis vertically

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and X-axis perpendicular to both axes. The calibrated space was approximately x = 1.0 m, y = 1.5

m and z = 0.5 m, and the root mean square error within the calibrated area of the measurement

system was < 1.0 mm.

Three-dimensional segmental data of the shank, foot and ball for each kicking trial were

computed from the raw coordinate data using a six degrees of freedom rigid body model (Visual3d

software, C-Motion Inc., USA). The six degrees of freedom rigid body model was determined

from static captures of the distal and proximal segment positions and tracking markers. The

location of the knee, ankle and metatarsophalangeal joints (1st and 5th) were determined from

markers attached to the medial and lateral aspect of each joint. Data were smoothed with a low

pass Butterworth filter with a cut-off frequency of 280 Hz. The choice of smoothing procedure

was based on previous literature that explored various cut-off frequencies within foot-ball impact

using residual analysis and visual inspection (Nunome, et al., 2006b; Peacock, et al., 2017a). To

accommodate for convention differences between left and right footed kickers, the direction was

reversed for all vector measures (kicking accuracy, azimuth ball flight trajectory, etc.) calculated

in the x-dimension of the global coordinate system for the left footed kickers. This ensured

positive values in the x-dimension of the global coordinate system corresponded to the lateral

aspect of the foot.

Initial ball flight characteristics were calculated within Visual3d and Microsoft Excel

from data calculated over five frames after ball release from the foot (Figure 8.1 and 8.2). Azimuth

ball flight trajectory and elevation ball flight trajectory were calculated from the X and Y, and Y

and Z velocity components of the ball geometric centre in the global coordinate system,

respectively (Figure 8.1A). Ball angle and angular velocity were calculated within Visual3d using

the rigid body model within the global coordinate system (Figure 8.1B). The kick position,

defined as the position of the ball at the first frame of ball release within the X-axis of the global

coordinate system, was also calculated to ensure any changes in this position were included in the

regression equation. This accounted for the scenario where a kick that was completed 1 meter to

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the lateral aspect of the target with an azimuth flight of 0° would correspond to a measured kick

accuracy of 1 meter.

Figure 8.1: Visual representation of ball flight characteristics. A) Ball flight trajectory. B)

Ball angular dimensions.

Foot-ball impact characteristics were calculated within Visual3d, Microsoft Excel and

Matlab software. The oblique impact theory indicates the trajectory and spin of an object after

impact is influenced by the surface angle of the two objects in the collision. In the context of

football kicking, the oblique impact theory indicates foot trajectory, foot velocity, ball impact

location, foot angle and ball angle will determine the ball flight characteristics. Therefore, we

measured these parameters. Foot trajectory was calculated from the centre of mass of the foot

over five frames prior to impact in the azimuth and elevation dimensions. Ball impact location

was calculated in three-dimensional space using a novel method (described below) that presented

the impact location as two coordinates, azimuth ball impact location and elevation ball impact

location. Foot angle, ball angle and foot-ball angle were calculated from the defined coordinate

system of each segment (Figure 8.2). Foot and ball angles were calculated in reference to the

global coordinate system, and foot-ball angle was calculated by the ball angle in reference to the

foot angle. Initial foot and ball velocity magnitudes were also calculated, however, given the task

was submaximal, there was little change in both foot and ball velocity for all players and these

parameters were removed from further analysis.

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A novel method was developed to calculate the impact location on the ball within three-

dimensional space using Matlab software and Microsoft Excel. Previous methods developed to

calculate impact location were not suitable for the present study, as a given impact location was

dependent upon the relative foot-ball displacement, the relative foot-ball angle, ball shape and

foot shape. The method reported by Ishii, et al. (2012) was developed for a spherical ball in two-

dimensional space, and the method by Peacock and Ball (2017) did not accommodate changes to

relative foot-ball orientation, foot-ball displacement, nor foot shape. Hence, a method to calculate

impact location, where each of these variables were included, needed to be developed. This was

achieved by modelling the foot and ball as rigid bodies and calculating the intersecting point at

ball contact. Because the foot and ball are not rigid bodies during impact, the developed method

to calculate impact location was not assessed during impact, but all impact characteristics were

measured at the instant of ball contact. Modelling of the foot and ball was achieved by geometric

equations of shapes that replicated the foot and ball. The foot was modelled as a semi-elliptical

cylinder that incorporated dimensions of the individual’s foot shape (Equation 8.1-4; Figure

8.2A). The ball was modelled as an ellipsoid using dimensions of the ball taken under a static

capture (Equation 8.5; Figure 8.2B). To calculate impact point on the ball, a 200 x 200 X-Y-Z

coordinate mesh was developed for the foot surface. This matrix of coordinates was then rotated

and translated in respect to the position of the ball, using the foot-ball angle and displacement.

Then, each coordinate of the foot surface was entered into the equation of the ball surface

(Equation 8.5) which solved the position of each coordinate relative to the surface of the ball. A

coordinate outside the shell of the ball solved a value > 1, a coordinate on the shell of the ball

solved a value = 1, and a coordinate within the shell of the ball solved a value < 1. The impact

point on the ball was calculated from the distance between the ball centre and the X-Y-Z foot

coordinate that yielded the smallest value when entered into Equation 8.5. Due to the ellipsoidal

shape of the ball, the distance between the ball centre and the impact point changes depending on

the impact location, unlike a soccer ball that has a constant radius. Therefore, the impact location

was presented as two angles from the centre of the rear point of the ball (Equation 8.6-7; Figure

8.3).

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𝑥𝑙 =𝑤𝑙

2cos ∅

Equation 8.1

Where xl = the x-coordinate of the foot grid for a given length of the foot; wl = the width

of the foot for a given length, calculated from Equation 2; θ = a vector comprising 200 linearly

spaced angles between 0° to 180°.

𝑤𝑙 =(𝑤𝑑 − 𝑤𝑝)

2 ∙ 𝑙∙ 𝑤𝑙 + 𝑤𝑝 Equation 8.2

Where wd = the width of the foot at the distal end of the segment; wp = the width of the

foot at the proximal end of the segment; l = the length of the foot.

𝑦𝑙 = ℎ𝑙 sin ∅ Equation 8.3

Where yl = the y-coordinate of the foot grid for a given length of the foot; hl = the height

of the foot at a given length.

ℎ𝑙 =(ℎ𝑝 − ℎ𝑑)

𝑙∙ ℎ𝑙 + ℎ𝑑 Equation 8.4

Where hp = the height of the foot at the proximal end of the segment; hd = the height of

the foot at the distal end of the segment.

𝑥𝑙2

𝑟𝑥2

+𝑦𝑙

2

𝑟𝑦2

+𝑙2

𝑟𝑧2

= 𝑑 Equation 8.5

Where rx = the short radius of the ball; ry = the short radius of the ball (note: rx = ry); rz =

the long radius of the ball; d = the depth of the coordinate relative to the ball shell.

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Figure 8.2: Surface models of the foot (A) and ball (B).

𝐵𝐼𝐿𝑒𝑙 = tan−1 (

−𝑦

−𝑧) Equation 8.6

Where BILel = ball impact location across the elevation plane; y = the distance between

impact location and the ball centre in the y dimension; z = distance between impact location and

ball centre in the z dimension.

𝐵𝐼𝐿𝑎𝑧 = tan−1 (𝑥

𝑦)

Equation 8.7

Figure 8.3: Measurement of ball impact location across the elevation plane (A) and the

azimuth plane (B).

θ° θ°

A B

y

y z

x

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To identify the relationship between ball flight characteristics and kicking accuracy (aim

1A), multiple linear regression analysis was performed. Because this analysis was based on the

ball during its flight, it was performed on all trials across all players. Only kicks successfully

caught by the receiving player were analysed as these were the only trials that kicking accuracy

could be reliably measured. Kicks that landed prior to reaching the target or kicks that travelled

overhead of the target were removed for this component of analysis. In total, 115 kicks were

included in the regression. The mean and standard deviations of these kicking trials were reported

to provide a summary of the ball flight characteristics and kicking accuracy. The multiple linear

regression was performed using the stepwise method. The dependent variable was kicking

accuracy, and the independent variables were azimuth ball flight trajectory, ball angular velocity,

ball angle, and kick position. One outlier was identified by calculating Mahalanobis distance using

a cut-off of p < 0.001 (Tabachnick & Fidell, 2001), leaving a total N of 114.

To identify the relationship between foot-ball impact characteristics and ball flight

characteristics (aim 1B), multiple linear regression analysis was performed within SPSS software

on an intra-individual level. To follow a systematic approach, and because ball azimuth flight

angle was the most important flight characteristic influencing kicking accuracy, we performed

the regression using only azimuth ball flight trajectory as the dependent variable. This was

performed on an intra-individual level to identify if the variance changed between players,

possibly due to individual techniques adopted during foot-ball impact. Ball impact location across

the azimuth and elevation dimensions, foot-ball angle (three dimensions) and foot trajectory

across the azimuth dimension were entered as the independent variables. Because Tabachnick and

Fidell (2001) recommend a 5:1 case: parameter ratio, and not all of the 30 kicks per player could

be analysed due to markers obstructed or moving out of the capture area, foot-ball angle was

calculated to replace foot angle and ball angle. The same regression analysis procedure was

performed as previously stated for the relationship between ball flight characteristics and kick

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accuracy. The mean and standard deviation of each individual for these impact characteristics and

for azimuth ball flight trajectory were additionally presented.

To determine if performance variability was associated with an increased or decreased

variability in foot-ball impact (aim 2), variability (standard deviations) of ball flight and foot-ball

impact characteristics were calculated of each player. Correlations were performed between

variability in standard deviation of azimuth ball flight trajectory and standard deviation of azimuth

ball impact location, and between standard deviation of azimuth ball flight trajectory and standard

deviation of foot-ball angle Y. The statistics of r, effect size (Cohen, 1988) and p-value were

calculated to describe the correlations.

8.3. Results

The relationship between ball flight characteristics and kicking accuracy was identified.

The mean and standard deviation of kicking accuracy and ball flight characteristics were

quantified (Table 8.1). The model identified from the stepwise regression identified 69.9% of

variance in kicking accuracy was explained by six ball flight characteristics (Table 8.2). The

standardised coefficients from the regression model identified azimuth ball flight trajectory was

most influential to the measurement of kicking accuracy; the standardised coefficient had a three-

fold greater effect on kicking accuracy than all other ball flight characteristics.

Table 8.1: The descriptive statistics of kicking accuracy and ball flight characteristics (N =

114).

Mean (std)

Kicking accuracy (m) 0.2 (1.5)

Azimuth ball flight angle (°) 1.6 (3.6)

Elevation ball flight angle (°) 22.3 (5.7)

Kick position (m) 0.2 (0.2)

Ball angle X (°) 0.6 (11.7)

Ball angle Y (°) -0.7 (8.5)

Ball angle Z (°) -4.1 (13.6)

Angular velocity X (rad/s) 26.0 (6.7)

Angular velocity Y (rad/s) 0.4 (5.0)

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Angular velocity Z (rad/s) 0.5 (8.5)

Table 8.2: Regression results of ball flight characteristics predicting kicking accuracy (N =

114).

Azimuth

ball flight

trajectory

Kick

position

Ball

yaw

angle

Ball

pitch

angular

velocity

Ball yaw

velocity

Elevation

ball angle Intercept

Coefficient 0.34 -1.95 0.03 -0.05 -0.03 -0.04 2.55

Standard

error (m) 0.03 0.50 0.01 0.02 0.01 0.02 0.66

Standardised

coefficient 0.84 -0.28 0.24 -0.24 -0.15 -0.17 -

The foot-ball impact characteristics and azimuth ball flight trajectory were quantified for

each player (Table 8.3). Foot-ball impact characteristics explained over 74% of variance in

azimuth ball flight trajectory for all players except one (Table 8.4). Azimuth ball impact location

was the only impact characteristics influential to all players, and produced the largest standardised

coefficients for all players. Further, azimuth ball impact location had greater than a two-fold effect

over the remaining impact characteristics in all players except one. Foot-ball angle Y was

influential in eight of the ten players, and the standardised coefficients were in the range of 0.16

– 0.48 in magnitude. Elevation ball impact location and foot-ball angle X were influential in two

players, and azimuth foot trajectory was influential in one player.

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Table 8.3: The mean and standard deviation of azimuth ball flight angle and kicking characteristics for all individuals.

Azimuth ball flight

angle (°)

Azimuth

foot

trajectory

(°)

Azimuth

ball impact

location (°)

Elevation ball

impact

location (°)

Foot-ball

angle X (°)

Foot-ball

angle Y (°)

Foot-ball

angle Z (°)

P01 (N = 27) 0.2 (5.0) 3.8 (1.3) 8.1 (7.3) 45.4 (4.4) 60.8 (8.1) -0.2 (10.6) 45.2 (12.3)

P02 (N = 24) -2.2 (4.4) 4.1 (2.0) 2.7 (5.4) 47.3 (2.5) 64.7 (3.2) -12.3 (6.8) 22.4 (8.8)

P03 (N = 25) -0.8 (3.6) 1.3 (2.2) 1.5 (2.9) 52.1 (3.3) 52.4 (6.5) -13.9 (4.1) -11.8 (8.0)

P04 (N = 29) 0.2 (3.2) 2.3 (2.0) 0.8 (3.6) 45.5 (2.6) 57.2 (3.9) -10.8 (4.4) 15.8 (7.5)

P05 (N = 22) 3.0 (3.6) 5.0 (1.8) -6.0 (4.1) 49.1 (2.0) 55.5 (4.5) -1.0 (4.1) 35.0 (9.1)

P06 (N = 25) 3.4 (3.0) 7.1 (1.1) -3.0 (3.7) 45.4 (3.6) 52.1 (4.0) -9.3 (4.4) 26.8 (9.0)

P07 (N = 25) -0.2 (6.3) 5.6 (1.8) -1.1 (5.6) 41.1 (5.1) 60.4 (8.5) -5.0 (7.7) -7.1 (12.3)

P08 (N = 28) 0.2 (2.6) 2.7 (1.6) 1.2 (2.3) 48.3 (4.5) 54.3 (3.6) -10.1 (5.0) 5.7 (8.0)

P09 (N = 25) 4.0 (4.0) 4.8 (1.1) -2.7 (4.6) 45.7 (4.6) 56.1 (6.0) -9.2 (6.1) 14.5 (10.4)

P10 (N = 20) -3.0 (3.2) 2.2 (1.4) 2.8 (3.4) 51.7 (4.2) 59.4 (7.0) -3.6 (6.2) 7.3 (11.0)

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Table 8.4: Regression results of foot-ball impact characteristics predicting azimuth ball flight trajectory. The coefficient (B), standard error

(σe) and standardised coefficients (β) of statistically significant (p < 0.05) foot-ball impact characteristics predicting azimuth ball flight

trajectory. Foot-ball angle Z was entered into the regression; however, this parameter was statistically non-significant and omitted from the

table.

Constant

Azimuth ball

impact location

(°)

Elevation ball

impact location

(°)

Foot-ball angle X

(°)

Foot-ball angle Y

(°)

Azimuth foot trajectory

(°) R-squared

P01

B 10.86 -0.54 -0.20

-0.07 0.75

90.2% σe 3.68 0.05 0.08

0.04 0.30

β

-0.79 -0.18

-0.16 0.19

P02

B -2.53 -0.79

-0.20

89.6% σe 0.64 0.06

0.05

β

-0.96

-0.31

P03

B -8.00 -1.08

0.11 -0.23

89.1% σe 2.17 0.10

0.04 0.07

β

-0.86

0.19 -0.26

P04

B -1.89 -0.70

-0.25

56.1% σe 1.14 0.12

0.10

β

-0.79

-0.34

P05

B -1.57 -0.76

74.9% σe 0.71 0.10

β

-0.87

P06

B -10.98 -0.71

0.18 -0.28

77.2% σe 4.27 0.09

0.08 0.08

β

-0.86

0.24 -0.41

146

P07

B 13.70 -1.13 -0.37

89.9% σe 3.59 0.08 0.09

β

-0.99 -0.30

P08

B -1.28 -0.84

-0.25

74.7% σe 0.60 0.11

0.05

β

-0.74

-0.48

P09

B 0.09 -0.76

-0.20

80.3% σe 0.74 0.08

0.06

β

-0.87

-0.31

P10

B -1.13 -0.90

-0.17

87.8% σe 0.36 0.08

0.04

β

-0.96

-0.33

A relationship was identified between variability in impact characteristics with variability

in kick outcome. The variability (standard deviation) of azimuth ball flight trajectory, the chosen

performance measure, differed between individuals (Table 8.5). The variability (standard

deviation) of azimuth ball impact location and foot-ball angle Y, the two most important foot-ball

impact characteristics explaining azimuth ball flight angle, also differed between players. There

was a relationship between the variability in foot-ball impact characteristics with the variability

in azimuth ball flight trajectory: significant positive correlations with very large effect sizes were

present between standard deviation in azimuth ball flight trajectory with azimuth ball impact

location (r = 0.80, p = 0.001) and with foot-ball angle Y (r = 0.71, p = 0.006).

Table 8.5: The standard deviations of azimuth ball flight trajectory, azimuth ball impact

location, and foot-ball angle Y for each player, ranked from lowest to highest using

azimuth ball flight trajectory as the performance indicator.

Ranking Player Azimuth ball flight angle Azimuth ball impact location Foot-ball angle Y

1 P08 2.6 2.3 5.0

2 P06 3.0 3.7 4.4

3 P04 3.2 3.6 4.4

4 P10 3.2 3.4 6.2

5 P03 3.6 2.9 4.1

6 P05 3.6 4.1 4.1

7 P09 4.0 4.6 6.1

8 P02 4.4 5.4 6.8

9 P01 5.0 7.3 10.6

10 P07 6.3 5.6 7.7

8.4. Discussion

How players attain accurate kicking in the Australian football drop punt kick is not fully

understood. Therefore, we determined how foot-ball impact influences kicking accuracy by

analysing 30m drop punt kicks at an intra- and inter-individual level. Firstly, we identified the

relationship between foot-ball impact characteristics, measured at the instant of ball contact, and

a measurement of kicking accuracy. The key result of this analysis was that azimuth ball flight

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trajectory was the most important ball flight characteristic, and azimuth ball impact location and

foot-ball angle Y were the two most important impact characteristics. Secondly, we also explored

variability in foot-ball impact characteristics to determine if kicking accuracy was obtained from

an increased or decreased variability. The key result of this analysis was the positive relationship

between absolute variability in impact characteristics (azimuth ball impact location and foot-ball

angle Y) and absolute variability in azimuth ball flight trajectory. These relationships indicate that

less performance variability was obtained by reducing variability in foot-ball impact

characteristics.

8.4.1 Biomechanical factors explaining kicking accuracy

Inaccurate kicking was mostly due to imparting the incorrect azimuth ball flight

trajectory. The standardised coefficient from the regression model for azimuth ball flight

trajectory had greater than a three-fold effect than the remaining ball flight characteristics on

horizontal kicking accuracy. Further, the sum of the standardised coefficients of the individual

ball flight characteristics that contribute the ball curve (ball orientation and ball spin) was 0.81,

still less than the standardised coefficient (0.84) for azimuth ball flight trajectory. Azimuth ball

flight trajectory and ball curve are two independent factors that will determine horizontal kicking

accuracy. Ball curve represents the deviation of the ball from its initial plane of projectile motion,

and is influenced by not only environmental conditions of wind, but also the aerodynamic forces

due to ball spin and in the case of the ellipsoidal ball sports, ball orientation. In particular, any

off-centred back-spin, such as a tilt about the yaw and roll ball angles, and angular velocity about

the yaw and roll ball angles, will produce an aerodynamic force pushing the ball off plane (Alam,

et al., 2009; Goff, 2013). In our analysis of the drop punt kick, the most important ball flight

characteristic for kicking accuracy were not those influential to ball curve, but azimuth ball flight

trajectory. This difference of influence was due to the magnitude of variability between the flight

characteristics that players produce in the drop punt kick, and how this magnitude of variability

influenced ball flight characteristics. Simply put, players can control ball curve more so than they

can control azimuth ball flight trajectory. This may be due to the shape of the foot and ball, where

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players ‘roll’ the ball up the foot during impact to apply the distinct back-spin. Therefore, while

it is still important for players to control factors influencing ball curve, these results indicate

inaccurate kicking was mostly due to imparting the incorrect azimuth ball flight trajectory.

The oblique impact theory applied through the duration of impact can be used to explain

the relationship between foot-ball impact characteristics and azimuth ball flight trajectory. The

oblique impact theory indicates the direction of travel of the ball after impact will be influenced

by the surface angle between the foot and ball during impact. When the surface angle between

the foot and ball and the trajectories of the foot and ball are perpendicular, the ball will be

propelled in the direction of the foot trajectory. The results from this study support the application

of the oblique impact theory. Azimuth ball impact location, measured at the instant of ball contact,

was the most influential impact characteristic to azimuth ball flight trajectory (Table 8.4). The

direction of the coefficient from the regression indicated medial impact locations on the ball

produced a lateral ball flight trajectory. As indicated by the oblique impact theory, an impact

location on the medial aspect of the ball is characterised by the perpendicular direction of the

surface angle pointing laterally from the foot direction of travel. Similarly, Peacock and Ball

(2017) found lateral foot impact locations translated to a lateral azimuth flight trajectory. Both

the present and previous studies recorded impact location at the instant of ball contact, not through

the duration of foot-ball impact. However, due to the mostly planar motion of the foot and ball

during impact (in the sagittal plane) and the alignment of the long axes of the ball and foot aligned

in the drop punt kick, the impact location across the medial-lateral aspect of the foot at the

beginning of impact mostly corresponds to the impact location during impact. Changes to foot-

ball angle Y can influence this relationship though. When the long axis of the ball is not aligned

with the long axis of the foot, the contact area between the foot and ball will spread across the

medial-lateral direction of the foot during impact. This is again supported by the direction of the

coefficient of foot-ball angle Y in the regression, that was negative in direction for all eight players

(Table 8.4). With a negative foot-ball angle Y, the top side of the ball is tilted laterally whereby

the impact location will spread onto the lateral aspect of the foot and/ or the medial aspect of the

150

ball. These results support the validity of the oblique impact theory applied through the duration

of impact to explain the relationship between foot-ball impact characteristics and azimuth ball

flight trajectory. Further examination of the dynamic contact area between the foot and ball is

made in Chapter 9.

8.4.2 The influence of variability on kicking accuracy

Decreased performance variability was associated with reduced variability in foot-ball

impact characteristics (Table 8.5), indicating players who produced less variability in foot-ball

impact characteristics produced less variability in azimuth ball flight trajectory. It is important to

note; the task goal was not to impart the lowest standard deviation in azimuth ball flight trajectory

but to kick to the target as accurately as possible. Players could have imparted an off-centred

azimuth ball flight trajectory that was offset by ball curve for some trials, whereby the standard

deviation for azimuth ball flight trajectory would be increased but with no change to the outcome

(kicking accuracy). Despite this, azimuth ball flight trajectory was chosen as the performance

measure because kicking accuracy could not reliably be measured for every kick (as a large

number of kicks for most performers fell short of or travelled over the target due to errors in the

vertical component) and only a small sample of kicks would have been available to determine the

relationship between variability in impact and performance variability (the measurement of kick

accuracy). Given the nature of the task analysed in the present study that required players to kick

straight from a confined kicking area, there was no benefit to use a ball curve, nor was it observed

that players did purposely use a ball curve. Furthermore, azimuth ball flight trajectory was the

most important ball flight characteristic to kicking accuracy. Therefore, to provide a strong sample

size for this analysis it was appropriate to use azimuth ball flight trajectory as the performance

measure. The positive relationship between standard deviation in impact characteristics and

standard deviation in azimuth ball flight trajectory indicates performance variability was reduced

by reducing variability in foot-ball impact characteristics.

It was expected that a functional use of variability in foot-ball impact characteristics

would have produced a high standard deviation in foot-ball impact characteristics with low a

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standard deviation in azimuth ball flight trajectory. The results of this study indicated that

performance variability was decreased with reduced variability in foot-ball impact characteristics.

This indicates variability in foot-ball impact characteristics was dysfunctional, similar to the

findings in golf by Betzler, et al. (2012, 2014). This is likely due to the extremely short duration

of impact and the timing of the reflexes in the human body. The monosynaptic reflex, the quickest

reflex in the body, is in the range of 20-40 ms between individuals (Latash, 2012). Given the

duration of impact in football kicking is approximately 10-12 ms (Peacock, et al., 2017a), far less

than the timing of the monosynaptic reflex, it is not possible for players to receive feedback just

prior to and during impact to make the necessary corrective changes. This might also explain why

better skilled golf players also reduce variability, as the contact time between golf head and ball

is less than 1 ms (Roberts, Jones, & Rothberg, 2001). Therefore, players can only impart the

desirable flight characteristics by impacting the ball with the exact necessary impact

characteristics.

8.4.3 General discussion

The results in this study and in previous work (Peacock & Ball, 2017) indicate there is

not one sole foot-ball impact characteristic that is a primary factor influential to kicking accuracy,

rather, kicking accuracy is influenced by the combination of impact characteristics. Dissimilarly,

Hennig (2011) stated there was one primary factor influential to kicking accuracy in the soccer

instep kick; the homogeneity of pressure between the shoe and ball. The homogeneity of the

pressure between the shoe and ball is influenced by bony prominences on the foot, and is

expressed by the difference in pressure between adjacent positions on the dorsal aspect of the foot

surface. Footwear designs that have thinner padding produce a non-homogenous pressure, as

pressure peaks are produced on the anterior surface of the foot due to bony prominences (Hennig

& Sterzing, 2010). The homogeneity of pressure between foot and ball, caused by bony

prominences and footwear designs, however, does not explain all aspects of football kicking

accuracy. In particular; why do players produce a breakdown of accurate and inaccurate kicks

while wearing the same shoe and kicking with the same foot, when the homogeneity of the

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pressure distribution between foot and ball (caused by bony prominences) will be constant?

Furthermore, adding padding on the surface of the foot to specifically produce a more

homogenous pressure was found to have a non-significant effect on kicking accuracy (Hennig &

Althoff, 2018). The results in this study indicate it is the combination of foot-ball impact

characteristics that is influential to kicking accuracy. As players produce variability in the

combination of impact characteristics, either functional or dysfunctional, the ball flight

characteristics change. Players must control all foot-ball impact characteristics to attain kicking

accuracy, such as impact location and foot-ball angle (where applicable depending on ball shape).

The results of this study identify the importance of precision when completing repetitions

of a kick with set task constraints. To improve performance in a consistent task, coaches should

provide specific feedback that assists players to reduce variability in impact location and foot-ball

angle (the two most important foot-ball impact characteristics). These results might indicate the

importance of training players to impact the ball with a consistent technique for all kicking tasks.

But, it has been argued that players should have the ability to functionally vary technique to allow

for perturbations in the environment, gameplay and task (Bartlett, et al., 2007; Ford & Sayers,

2015). It could not be determined how players adapt foot-ball impact to satisfy different task

constraints because only one set of task constraints was analysed in this study.

The results in this study identify better performance was achieved by reducing variability

in impact characteristics, which asks the question of where does variability exist throughout the

kicking skill to functionally assist in delivering the kicking foot to the appropriate position on the

ball. Future work is required on the coordination between the body and ball in the lead up until

impact, such as coordination between the foot and ball during the forward swing. Functional

variability might exist in foot-ball impact characteristics, but, it is clear players cannot adapt their

impact characteristics during the extremely short impact phase of the kick. However, it is likely

players functionally vary impact characteristics between kicking tasks, such as different approach

angles. Future work is required to understand variability in foot-ball impact characteristics

between different kicking tasks.

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The limitations of this work were the assessment of kicking accuracy (measured only in

the horizontal plane) and the methods used in the regression statistics. In gameplay of Australian

football and other football codes, accurate kick outcomes are often also constrained in the vertical

dimension. This is exemplified in Australian football by a successful pass requiring the ball does

not travel over or fall short of the desired team member. In other football codes, such as soccer

and rugby, the ball must also travel underneath or over the horizontal crossbar, respectively.

Future work should investigate the causes of errors in the vertical dimension of kicking accuracy.

Another limitation of the present study was the multiple regression statistics. While the multiple

regression statistics did identify the influence of each individual impact characteristic, it was also

necessary to reduce the number of analysed parameters due to the limited sample sizes (small

number of performed and subsequently analysed kicks). An example of this is combining

individual foot and ball angles into foot-ball angle. Important information regarding foot and ball

angles might have been lost due to this process. Having a larger number of kicks to be analysed

would have permitted the inclusion of more variables in the statistical models and could have

been achieved by pooling all kicks into one large data set. But, given differences in each players

foot shape existed and individual techniques may have been employed, it was not appropriate to

pool all trials together as the data would no longer have been independent. Furthermore, the use

of linear statistics may have concealed the measured influence of some parameters toward the

dependent variables that are non-linear.

8.5. Conclusion

The aim of the present study was to identify the characteristics that influence accurate

kicking. Kicking accuracy within the drop punt kick, measured as the horizontal distance between

the target and the outcome, was mostly explained by azimuth ball flight trajectory and not factors

associated with ball curve. From this, azimuth ball impact location and foot-ball angle Y were

identified as the most important impact characteristics influencing azimuth ball flight trajectory.

Variability existed within and between players during kicks as they completed the accuracy based

154

task. It was identified less variability in the performance measure was attained by producing less

variability in impact characteristics.


The aim of the present study was to identify how foot-ball impact characteristics influence

kicking accuracy. These results contribute to answering aim 2 of the overall thesis. Previous

chapters with the mechanical kicking machine identified ball angle, impact location and foot

trajectory each influenced ball flight characteristics. The present study, identified using human

kickers, support these previous findings. The full discussion of impact influencing kicking

accuracy is found in section 10.2.2. An important finding of the present thesis is the dynamic

nature of the contact area between the foot and ball during impact. The present chapter identified

this dynamic nature explained some key results, such as the influence of foot-ball angle Y on

azimuth ball flight angle. Building on from this finding, Chapter 9 aimed to quantify this dynamic

motion of the contact area between the foot and ball.

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Chapter 9: Study 7 - The contact area between foot and ball

during impact

Abstract: During foot-ball impact, it has been qualitatively observed that the ball

‘rolls’ up the foot. This ‘rolling’ motion visually appears to contain a change in ball

angle and the impact location on the foot moving proximally. An important step in

this thesis is to quantitively measure this occurrence, due to its importance in

explaining some of the key results. Therefore, the aim of this chapter was to quantify

the contact area between foot and ball during impact: measure the magnitude of ball

deformation of an ellipsoidal ball and the impact location on the foot. This was

achieved by re-analysing data from Chapter 6 and expanding the pre-developed two-

dimensional model to calculate impact location throughout the duration of impact

and calculate the magnitude of ball deformation. The results from this analysis

confirmed the qualitative observation of the ball rolling up the foot: during impact,

ball angle increased and the impact location on the foot moved proximally. This

result can explain several findings within the present thesis on kicking accuracy and

further expand our knowledge on ankle motion during impact.

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9.1. Introduction

Analysis of the foot-ball impact phase in kicking has been performed by using initial,

final, and average discrete parameters of impact, by measuring time-series data during impact by

recording data at high sampling frequencies (> 2,500 Hz), or, by using a combination of both

discrete and time-series parameters. Calculating parameters during impact can be difficult due to

the deformation of the foot and ball. Several authors have developed methods that can measure

deformation of the foot and ball, whereby identifying the unique motion of the foot and ball during

impact has been identified. Some notable findings from this analysis of the impact phase include:

the transfer of energy from foot to ball occurs over the first three-fourths of impact duration, not

the entire duration of the phase (Peacock, et al., 2017a; Shinkai, et al., 2009); while most players

are forced into distinct plantarflexion by the end of impact, the ankle motion during impact of

most individuals features an initial movement of dorsiflexion prior to plantarflexion (Peacock, et

al., 2017a; Shinkai, et al., 2009); and, several authors have developed methods that can calculate

instantaneous force during impact in order to understand the risk of injury (footballer’s ankle)

(Iga, Nunome, Inoue, & Ikegami, 2013; Iga, et al., 2017; Shinkai, et al., 2009; Tol, et al., 2002).

Within this thesis, foot-ball impact has primarily been analysed by using the pre- and post-

conditions of impact, whereby the relationship between initial impact conditions and ball flight

characteristics has been identified. Additional analysis of the what occurs during impact has been

performed for unexpected results; for example, ankle plantarflexion was identified to decrease at

higher foot velocities despite a greater external torque applied to the joint ankle, where it was

identified the initial dorsiflexion motion had increased (Chapter 6.4.1 ).

Anecdotal observations of the video files from impact foot-ball impact have identified

the ball ‘rolls’ up the foot during impact. Given the transfer of velocity from foot to ball has

previously been identified to occur not instantaneously, but over three-fourths of impact,

understanding how the ball moves on the foot during impact can help further understand the

interaction. Anecdotal observations of video files from foot-ball impact over the past five years

by the author of this thesis has identified the contact area during impact is dynamic: it increases

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in size with deformation and translates as the ball changes angle. These anecdotal observations

can explain the results from this thesis that could not be explained solely by changes to the

characteristics at the start of impact. In Chapter 8, the multiple linear regressions indicated a

systematic shift in foot-ball angle Y will alter azimuth ball flight trajectory, despite the surface

angle at the beginning of impact being consistent due to not change in the impact location. The

observation of the ball rolling up the foot, however, can explain this result. With a shift in the

foot-ball angle Y, the direction of the ball ‘rolling’ up the foot along the longitudinal axis of the

ball will be at an angle to either the medial or lateral sides of the foot. This result indicates that

what occurs during impact, not solely at ball contact, is influential to kick outcome.

An important step within this thesis is to quantify the anecdotal observations of the ball

‘rolling’ up the foot during impact. The key theory identified within this thesis on kicking

accuracy, whereby the surface angle between foot and ball throughout the duration of impact

influences the direction of the force vector applied to the ball, currently does not have quantitative

evidence supporting all results. By quantifying the anecdotal observation of the ball ‘rolling’ up

the foot, evidence will be provided to support the notion of the surface angle during foot-ball

impact and not just at the beginning of impact influences the outcome of the kick. Therefore, the

aim of this chapter was to quantify the contact area on the foot during impact of an ellipsoidal

ball: develop and validate a method to calculate the magnitude of ball deformation and the change

in impact location on the foot.

9.2. Methods

The previously established method within this thesis to calculate impact location two-

dimensionally was expanded throughout the duration of impact. Given the method was based on

the static non-deformed size of the foot and ball, it was not appropriate to use this on the human

kickers due to the deformation of the foot, or, more appropriately, change in shape of the

impacting surface of the foot (Asami & Nolte, 1983; Nunome, et al., 2014). This method could,

however, be used on the mechanical kicking machine because deformation of the foot did not

158

occur. The data from Chapter 5 (comparison of rigid to non-rigid ankles) were reanalysed and

impact location was calculated throughout the entire duration of impact.

9.2.1 Data collection

Two-dimensional sagittal plane data were collected from high-speed video (Photron SA3,

Photron Inc., USA, 4,000 Hz, resolution 768 x 512 pixels) zoomed to include just the kicking

area. Tracking markers (12.9 mm spherical and 8 mm flat) on the limb and ball were tracked from

20 frames before ball contact to 20 frames after the ball had left the boot (identified visually from

the video) using ProAnalyst software (Xcitex Inc., USA). To eliminate movement of the boot

influencing foot and ankle data, the foot tracking marker was attached directly to the fifth

metatarsal by cutting a hole in the boot and tapping a thread into the foot. This marker was also

occluded for approximately 10 frames through the middle of the tracking stage as it passed

through the tee supporting the ball, and these points were interpolated within the tracking

software. Raw X and Y coordinates were exported to Visual3d software (C-Motion Inc., USA) to

be analysed with a custom-made pipeline. Firstly, virtual markers were computed using the

method from Peacock, et al. (2017a) (Figure 9.1). All raw X-Y coordinates were then exported to

Matlab software (R2016b, The Mathworks Inc., USA) to calculate ball deformation by modelling

the foot and ball.

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Figure 9.1: Orthogonal reference and tracking and virtual markers of the limb and ball.

Virtual markers are represented by the grey outline of the circular markers.

9.2.2 Deformation of an ellipsoidal ball and calculation of impact location

The dorsal aspect of the foot/ boot was modelled as a linear line (LL), between the points

ShBx,y and FBx,y (Figure 9.2). Only the foot/ boot segment was included within the model as

the point of maximal deformation was identified, both initially qualitatively and subsequently

quantitatively, to not occur on the shank for the present study. The coordinates of any point along

the most antero-dorsal aspect of the foot could be computed by entering in either the x or y value

into Equation 9.1, to yield the residual coordinate.

𝐿𝐿𝑦 = 𝑚 ∙ 𝐿𝐿𝑥 + 𝑏1 Equation 9.1

Where; LLy = the y-coordinate along the dorsal aspect of the foot, LLx = the x-coordinate

along the dorsal aspect of the foot, and;

° 3 x ball

tracking

markers

4 x ball virtual

markers

3 x foot tracking

markers FC

Ball angle. Arrow indicates

negative direction.

x, direction of kick

y

ShT

ShB

FB

160

𝑚 = (𝐹𝐵𝑦 − 𝑆ℎ𝐵𝑦)

(𝐹𝐵𝑥−𝑆ℎ𝐵𝑥) Equation 9.2

𝑏1 = 𝑚 ∙ −𝐹𝐵𝑥 + 𝐹𝐵𝑦 Equation 9.3

Figure 9.2: Location of landmarks

For the remainder of the foot and ball model, the x-coordinates (LLx) were treated as an

independent variable, with an infinite number of points between the positions of ShBx and FBx.

Secondly, as identified by Ishii, et al. (2009), deformation is best represented as displacement

between the foot and ball running as a vector in the perpendicular direction to the linear line

representing the foot (Figure 9.3). This vector can be computed using Equation 9.4, and also

requires the x-coordinate on the dorsal aspect of the foot.

ShBx,y

LLx,y

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Figure 9.3: Representation of foot and ball model

𝑃𝐿𝑦 = 𝑛 ∙ 𝑃𝐿𝑥 + 𝑏2 Equation 9.4

Where; PLy = the y-coordinate of the perpendicular line, PLx = the x-coordinate

of the perpendicular line, and;

𝑛 = −𝑚−1 Equation 9.5

𝑏2 = −𝑛 ∙ 𝐿𝐿𝑥 + 𝐿𝐿𝑦 Equation 9.6

To calculate the displacement between the foot and the ball, the intersecting point

between the perpendicular line and the shell of the ball needed to be calculated. This was achieved

by modelling the ball as an ellipse (Equation 9.7), adjusting for rotation of the ball (Equation 9.8)

Linear line

162

and translation of the foot and ball in space (Equation 9.9), solving Equation 9.4 (with updated

field of Equation 9.9) into Equation 9.7, and then finally using the quadratic equation (Equation

9.10) to find the intercepting point. The quadratic equation yields two points, because a linear line

passes through an ellipse at two points. But, because the foot always impacted the ball in the

bottom left quadrant, due to the direction of the kick and the placement of the camera (right hand-

side sagittal plane), only the ‘-‘ sign was needed. Equation 9.11 will yield the x-coordinate of the

intersecting point, and solving this into Equation 9.4 will yield the y coordinate. Lastly, to

calculate the resultant displacement between the foot and ball, Equation 9.11 will find the

displacement.

(𝑥)2

𝑅𝑥2 +

(𝑦)2

𝑅𝑦2 = 1 Equation 9.7

Where; x = the x-coordinate of the ball shell, y = the y-coordinate of the ball shell, Rx =

short radius of the ball and Ry = long radius of the ball.

[𝑥′𝑦′

] = [𝑐𝑜𝑠𝜃 𝑠𝑖𝑛𝜃

−𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃] [

𝑥𝑦] Equation 9.8

Where; x’, y’ = the new ball shell position and replace x, y in equation 9, and θ is the ball

orientation.

𝑏3 = 𝑏2 + (𝑛 ∙ 𝐵𝐶𝑥 − 𝐵𝐶𝑦) Equation 9.9

Where; BCx,y = ball centre x-coordinate, y-coordinate.

𝑃𝑆𝑥 = −𝑏 ± √𝑏2 − 4𝑎𝑐

2𝑎+ 𝐵𝐶𝑥 Equation 9.10

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Where a = x2 constants, b = x constants and c = constant. Note BCx has been added as

part of the translation process.

𝐷𝑒𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 = √(𝐿𝐿𝑥 − 𝑃𝑆𝑥)2 + (𝐿𝐿𝑦 − 𝑃𝑆𝑦)2 Equation 9.11

Where LLx,y = the x,y-coordinates along the dorsal aspect of the foot; PSx,y are the x,y-

coordinates of the perpendicular line (equation 6) intercepting the shell of the ball (equation 9),

with updated terms of equation 10 and 11 to account for ball rotation and translation, to be finally

solved using the quadratic formula (equation 12).

These steps will yield the deformation of any point along the dorsal aspect of the foot.

Plotting Equation 9.11 as a function for LLx between the points of ShBx and FBx will yield a

parabola, and its’ maximum will yield the point of maximum deformation across the dorsal aspect

of the foot, and was chosen as the impact point on the foot. Impact location was calculated using

Equation 9.12 (Figure 9.4).

𝐼𝑚𝑝𝑎𝑐𝑡 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 = √(𝐿𝐿𝑥 − 𝐹𝐶𝑥)2 + (𝐿𝐿𝑦 − 𝐹𝐶𝑦)2 Equation 9.12

164

Figure 9.4: Foot and ball model, 25 frames into contact (near the point of maximal

deformation). The points ILx,y and PSx,y represent the x-y coordinates of the impact

location on the foot and the maximum displacement between the foot and ball shell in the

perpendicular direction, respectively. The solid linear line between the points ShBx,y and

FBx,y represent the dorsal aspect of the foot and the dotted linear line between the points

ILx,y and PSx,y is the deformation distance. All other points have been previously defined.

9.2.3 Parameter calculation

The profile of impact, comprising foot velocity, ball velocity and the magnitude of ball

deformation, were calculated for each ankle configuration. The mean and standard deviation of

the 10 trials for each condition were calculated. Foot velocity was calculated as the first derivative

of the virtual marker FC. Ball velocity was calculated from the first derivative of the virtual

marker BC, representing the geometric, undeformed centre of the ball. The magnitude of ball

deformation was calculated from Equation 9.11.

Ball angle and impact location were calculated throughout the duration of impact. The

mean and standard deviation of the 10 trials for each condition were calculated. Ball angle was

calculated from the BC and BT markers and calculated in the global coordinate system with the

counter-clockwise direction representing the positive direction (Figure 9.2). Impact location was

calculated along the most antero-dorsal aspect of the foot in relation to the FC along the proximal-

distal direction. A distal impact location was represented as a positive value.

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A video overlay of the foot and ball model was created to provide a visual analysis of the

foot and ball model. This analysis provided a visual representation of how the models performed

during impact in relation to the anecdotal observation of the ball rolling up the foot during impact.

The models representing the foot and ball and the location and magnitude of ball deformation

were plotted as overlays on top of the original video file of one kicking trial. Due to the print

nature of this Chapter within this thesis, a video could not be presented. However, to still include

this analysis, five screenshots were taken at key events: 1 frame prior to ball contact, at ball

contact, at the point of maximal deformation, 1 frame prior to ball release, at the point of ball

release. The results of this analysis were presented for one kick.

9.3. Results

Similar impact profiles were identified for the non-rigid and rigid ankle settings, and only

the non-rigid ankle was presented to reduce repetition. Maximal deformation occurred prior to

the crossover of foot and ball velocity (Figure 9.5). Impact location on the foot moved proximally

and ball orientation increased during impact (Figure 9.6). The magnitude of ball deformation,

calculated frame by frame for one video file, with images from the respective video file at five

points in time are presented in Figure 9.7.

Figure 9.5: The profile of impact. Foot velocity (solid black line; primary axis), ball

velocity (grey line; primary axis) and ball deformation (dashed black line; secondary axis)

through the duration of impact.

166

Figure 9.6: Ball orientation (solid black line; primary axis) and impact location (dashed

black line; secondary axis).

167

Figure 9.7: Ball deformation and corresponding video images at five points in time for one

particular trial. Images A and E are the immediate frame prior to ball contact (B) and

after ball release (E).

9.4. Discussion

The impact location on the most antero-dorsal aspect of the foot moved proximally during

impact, quantifying the anecdotal observations of the ball ‘rolling’ up the foot. The calculation of

ball deformation and impact location was made on the most antero-dorsal aspect on the foot,

where the anecdotal observations of the ball ‘rolling’ up the foot is quantified by the change in

impact location to the proximal direction and the increase in ball angle (Figure 9.6). At the most

antero-dorsal aspect of the foot, where the linear line was projected from, the ball would have

A

B

C

D

E

168

been mostly flatly deformed across the length of the foot due to the mostly linear surface and rigid

properties of the foot. It can be qualitatively visually analysed in Figure 9.7C the edge of the ball

extends beyond the linear line representing the most antero-dorsal aspect of the foot toward the

original, undeformed shell of the ball. This might indicate the linear line did not represent the

deformation, whereby the magnitude of ball deformation is overstated. However, due to viewing

ball deformation from the sagittal view, the non-flat deformation of the ball across the medial-

lateral direction occludes the true position of the antero-dorsal aspect of the foot. The ball is not

flatly deformed during impact across the medial-lateral direction due to the three-dimensional

geometric properties of the foot, corresponding to the depth within the cameras field of view. The

foot surface across the medial-lateral direction can loosely be described as a semi-spherical/ semi-

ellipsoidal shape (discussed more in the methods of Chapter 8 and 9), and the qualitative visual

analysis of the video file (Figure 9.7C) indicates the ball ‘wraps’ around this surface. This

occludes the view of the most antero-dorsal aspect of the foot, explaining why it visually appears

the measurement of ball deformation is overstated. However, given the rigid properties of the

foot, it can be assumed the most antero-dorsal aspect of the foot is non-deformed, where the

measurement of ball deformation along this plane of the foot is not overstated. Therefore, the

anecdotal observation of the ball ‘rolling’ up the foot is quantified by the impact location on the

foot moving proximally during impact as the ball changes its angle.

The profile of impact indicated that the point of maximal ball deformation occurred prior

to the crossover of foot and ball velocity (Figure 9.5), which represents a point of difference to

impact of a soccer ball. Shinkai et al (2009) and Tsaousidis & Zatsiorsky (1996) identified the

point of maximal deformation occurred when foot and ball velocity were equal. It is logical to

expect maximum deformation to occur when foot and ball velocity are equal because prior to this

point the foot is travelling faster than the ball, thus deforming it, and after this point the ball is

travelling faster than the foot, thus it is reforming. The different profile found for the AF ball used

in present study is likely due to its shape and motion during impact where it ‘rolls up’ the foot.

Based on the change in ball orientation and impact location on the foot evident during impact

169

(Figure 9.6), the area of intersection between the foot and ball is changing. The stiffness of non-

round and ellipsoidal shaped balls change depending on where it is deformed due to their non-

constant radius. Under a quasi-static measurement of ball stiffness, Holmes (2008) identified the

stiffness of a rugby league ball was greater when compressed on the belly compared to the point,

due to the ‘shape factor’ of the deforming ball changing. When comparing the belly to the point

of the ball, stiffness would be reduced at the point because a smaller area of the ball is being

deformed. For example, a 3 cm deformation on the point of the ball is equal to an area of

approximately 5.7% in the sagittal plane, compared to 11.5% when the belly of the ball is also

deformed 3 cm. When the ball rolls up the foot and the belly is impacted, a different part of the

ball is being impacted and the ‘shape factor’ is changing, increasing the stiffness of the ball.

During impact of a soccer ball there would be no change in ball stiffness if it were to roll up the

foot, as there is no change in ‘shape factor’ due to the spherical shape. The point of maximal

linear ball deformation in the sagittal plane can logically be considered to occur at the crossover

of foot and ball velocity for a spherical ball. The point of maximal linear ball deformation in the

sagittal plane for a non-round ball will be dependent upon the change in ball orientation during

impact: if there was no change in ball orientation maximum linear ball deformation will occur at

the crossover of foot and ball velocity, as indicated by the results of a soccer ball where the ball

radius is constant (Shinkai, et al., 2009); if the ball orientation is changing toward the belly, the

maximum linear ball deformation will occur prior to the crossover of foot and ball velocity as

seen in Figure 9.5. Future work should explore the timing of maximum linear ball deformation

for an ellipsoidal ball if the orientation was changing toward the point: these results indicate the

maximum linear deformation will occur after the crossover of foot and ball velocity. This also

indicates future work modelling an ellipsoidal ball to calculate deformation should calculate the

area in the sagittal plane. Or, even more appropriately, the volume of deformation in three-

dimensional space to measure the ball centre of gravity during impact rather than the linear

displacement. The difference between the relative timing of maximal deformation between impact

of an ellipsoidal ball and a spherical ball is due to differences in the shape of the balls.

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The formation of ball flight characteristics occurs through the duration of impact. Given

the increase in ball speed occurs over three-fourths of impact duration (Peacock, et al., 2017a;

Shinkai, et al., 2009), it can be logically expected the formation of other ball flight characteristics

to also occur over a duration of ball contact. The results of the ball angle during impact also

indicates the formation of ball flight characteristics occurs over the duration of impact and not

instantly. Interestingly, the change in ball angle ceased prior to three-fourths of impact duration

as previously identified for ball velocity: post-hoc analysis of ball angular velocity identifies the

increase in velocity reduced substantially at approximately 40% of impact duration, and actually

decreased in magnitude at approximately 70% of impact duration (Figure 9.8). This pattern of

ball angular velocity differs to the relatively uniform increase and plateau in ball translation

velocity observed in both this Chapter (Figure 9.5) and previous analyses (Peacock, et al., 2017a;

Shinkai, et al., 2009). This could be explained by several factors: the change in ball orientation

on the foot during impact and the pressure applied from ball to foot due to ball deformation. The

orientation of the ellipsoidal ball influences the torque applied to the ball, as identified previously

in Chapter 4.4.3 . As the ball orientation changes during impact, the torque applied from foot to

ball will also change. During impact the change in ball orientation corresponded to the long axis

of the ball is becoming more parallel to the surface angle along the length of the foot (Figure 9.9).

It was previously identified under both parallel and perpendicular foot surface – ball long axis

orientations that ball angular velocity was 0°/s (Chapter 4.4.3 Ball orientation about the x-axis;

Figure 9.10). A second explanation of the reduction in ball angular velocity during impact is that

as the ball is deformed onto the foot surface, a pressure is applied from the ball onto the foot.

Analysis of the deformation area can indicate the pressure distribution, whereby the pressure

along the foot surface during the deformed area will produce a torque both positive and negative

in the global coordinate system. Assuming the ball deformation applies a force in the

perpendicular direction to the surface of the foot along its length, the direction and location of the

force vector can be qualitatively analysed and is applied to both aspects about the ball centre

(Figure 9.11). The angular velocity of the ball will decrease if the net torque applied to the ball is

in the negative direction, whereby the force vector (the net pressure applied between foot and

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ball) is applied superior to the ball centre of mass. Future work is required to quantify this pressure

analysis, whereby the use of a force plate foot segment on the mechanical kicking machine can

provide true force measurements that will be invaluable for the analysis of energy transfer from

foot to ball. It can be seen; however, the formation of ball flight characteristics occurs through the

duration of impact whereby the change in impact location and ball orientation influences the

interaction.

Figure 9.8: Ball angular velocity during impact (mean = black line; standard deviation =

grey lines).

0

1000

2000

3000

4000

5000

0 20 40 60 80 100

Bal

l an

gula

r vel

oci

ty (

°/s)

Impact duration (0 - 100%)

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Figure 9.9: Change in foot surface – ball long axis orientation during impact. Comparisons

are provided at the instance of ball contact (A) and approximately three-fourths of impact

duration (frame 30 of 44) (B).

Figure 9.10: A snapshot at foot-ball contact when ball angular velocity was 0°/s because

the foot surface and ball long axis were parallel (Chapter 4.4.3 Ball orientation about the

x-axis).

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Figure 9.11: Estimation of force direction from ball deformation acting perpendicular to

the foot surface.

The results in this chapter support the explanations for the results within this thesis that

have relied on a qualitative analysis. It was identified in this chapter that the impact location

moves dynamically during impact. The multiple linear regression in Chapter 8 identified increases

to foot-ball angle Y translated to lateral azimuth ball flight trajectories. If all conditions of impact

were held constant but with a systematic increase in foot-ball angle Y, there would be no change

to the surface angle at the beginning of impact. This provides evidence against the surface angle

at the beginning of impact influencing the outcome, the key theory identified within this thesis to

explain differences in kicking accuracy. The result within this Chapter, whereby the impact

location moves dynamically during impact, supports the expansion of the impact location

throughout the duration of impact. It can be speculated that increases to foot-ball angle Y (where

the top of the ball is tilted laterally) will change the direction of the impact location to move

laterally on the foot during impact. As the impact location moves laterally, the surface angle of

the foot points laterally from the direction on the kick, explaining why azimuth ball flight

trajectory changes with foot-ball angle Y. This result provides evidence for the theory identified

within this thesis that the surface angle during impact influences the azimuth ball flight trajectory.

Direction of force from ball deformation/ pressure

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Future analysis should be performed in three-dimensional space to directly confirm the dynamic

nature of impact location moving medial-laterally.

Shinkai, et al. (2009) hypothesised the impact location on the foot moved distally in the

soccer instep kick. After first recording the impact phase at a sample rate (5,000 Hz) capable of

identifying the interaction during impact, they observed the ankle moved into initial dorsiflexion

prior to distinct plantarflexion. They hypothesised the impact location was proximal from the foot

centre of mass at the initial period of impact to produce the initial dorsiflexion, followed by the

impact location then moving distally onto the distal side of the foot centre of mass to produce

plantarflexion. In Chapter 6 (where the present data set came from), it was similarly identified the

ankle was produced initial dorsiflexion before the distinct plantarflexion. The result within this

chapter identifies the impact location moved proximally throughout the duration of impact,

indicating the ankle motion pattern of initial dorsiflexion followed by plantarflexion observed

within Chapter 6 was not due to the impact location on the foot during impact transitioning from

the proximal to distal side of the foot. Rather, the initial dorsiflexion motion was due to the ankle

containing an initial dorsiflexion angular velocity at the beginning of impact. The impact location

in the sagittal plane was measured to occur distally from the ankle joint onto the foot segment, as

measured by the point of maximal deformation on the most antero-dorsal aspect of the foot. This

impact location produces an external plantarflexion ankle torque, which first reduces the

dorsiflexion ankle angular velocity before increasing the plantarflexion angular velocity. It could

be speculated a similar mechanism may have occurred in the study of Shinkai, et al. (2009),

whereby the ball reaction force was applying a plantarflexion ankle torque. However, to further

understand the factors that influence ankle motion during impact of soccer kicking, future work

with the mechanical kicking machine that quantifies the direction of impact location and change

in ball angle during impact with a soccer ball should be performed to provide direct evidence.

The results within the present chapter have practical implications. As the contact area is

dynamic, i.e. it is constantly changing throughout foot-ball impact, players must control this

dynamic nature to ensure they impart the desirable ball flight characteristics. As identified within

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the present thesis and this chapter, key parameters such as foot-ball angle influence this dynamic

behaviour of foot-ball impact. Players and coaches must be aware of the importance of foot-ball

angle on the dynamic nature of kick to ensure they kick successfully.

9.5. Conclusion

The aim of this chapter was to quantify the anecdotal observation of the ball ‘rolling’ up

the foot during impact. By extending the developed method within this thesis to calculate impact

location throughout the duration of impact, the motion of an ellipsoidal ball ‘rolling’ up the foot

was quantified. This observation was quantified by the impact location moving proximally along

the foot and the ball increasing its angle (as calculated in the global coordinate system) during

impact.


The present chapter contributed to the overall thesis by quantifying the dynamic motion

between the foot and ball during impact. This dynamic motion has implications for how individual

foot-ball impact characteristics influence impact efficiency, ankle motion during impact, and ball

flight characteristics (aims 1 and 2 of the overall thesis).

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Chapter 10: General discussion

Successful football kicking is achieved by players imparting an appropriate combination

of flight characteristics onto the ball by impacting the ball with their foot. This thesis explored

the relationship between foot-ball impact phase and kick outcome. Critical review of the literature

identified two key areas of the relationship between foot-ball impact characteristics and kick

outcome that required further exploration: the influence of impact characteristics on ankle

plantarflexion, impact efficiency and ball velocity; and the influence of foot-ball impact

characteristics on ball flight characteristics and kicking accuracy. These two issues were explored

via two key experimental designs: systematic analysis with a mechanical kicking machine and

intra-individual analysis with human players.

10.1. How do foot-ball impact characteristics influence impact efficiency and

ankle plantarflexion

Foot-ball impact characteristics influenced ankle plantarflexion, impact efficiency, and

ball velocity, as identified from both the mechanical kicking machine and the human kickers. For

the mechanical kicking machine, systematic changes to individual impact characteristics

translated to changes in ankle motion, impact efficiency, and/ or ball velocity. For the human

kickers, impact efficiency and ankle plantarflexion was identified to differ between kicks due to

variation in foot-ball impact characteristics. Further comparisons between players also identified

how physical characteristics influenced ball velocity. From these analyses, the effectiveness of

reduced ankle plantarflexion as a coaching cue was determined, and impact efficiency was

influenced by the physical mass of the performer, impact location between foot and ball, ball

orientation, and ankle stiffness.

10.1.1 The influence of foot-ball impact characteristics on impact efficiency

10.1.1.1 Physical mass of the performer

The physical mass of the performer influences impact efficiency. Post-hoc analysis

between the physical mass of the individual players and the mean foot-ball speed ratio for all

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kicks identified increasing physical mass increased impact efficiency (r = 0.72; p < 0.01). This

has been previously identified by Andersen and colleagues and by Shinkai and colleagues

(Andersen, et al., 1999; Shinkai, et al., 2013). Increasing the physical mass of the striking limb

via weights, however, has been identified to have no effect on ball velocity because foot velocity

reduces (Amos & Morag, 2002; Moschini & Smith, 2012). However, no work has determined the

longer-term effect of increased shoe mass on foot velocity and ball velocity, whereby a longer

exposure to increased foot mass may assist in an increased strength and/ or coordination pattern

that increases the final foot velocity. Future work should explore this area to determine if it is an

effective strategy of improving kicking performance.

10.1.1.2 Proximal-distal impact location

Impact efficiency was influenced by proximal-distal impact location in the mechanical

kicking machine and in seven of ten human kickers. For the rigid ankle of the mechanical kicking

machine, distal impact locations increased impact efficiency because the linear velocity at the

impacting point increased with no increase to ankle plantarflexion. For the non-rigid ankle,

however, distal impact locations reduced impact efficiency because the ankle was forced into a

greater magnitude of ball velocity. In the human kickers, an optimal relationship was identified

in four players, a positive relationship was identified in two players and a negative relationship

was identified in one player. These results identify that proximal-distal impact location for both

the mechanical kicking machine and the human kickers was influential to impact efficiency.

Differences did exist between the mechanical kicking machine analyses and within the

human players as to what impact location produced the highest impact efficiency. Ishii and

colleagues (Ishii, et al., 2009, 2012) identified an optimal impact location on the foot in their

analyses of the soccer instep and soccer sidestep kicks. The results in this thesis, while an optimal

relationship was only identified in four of the human kickers, do not oppose an optimal

relationship between proximal-distal impact location with impact efficiency. For the mechanical

leg, not all impact locations were analysed. For the rigid ankle, the optimal is likely to exist along

the distal direction at a location where the contact area between foot and ball is compromised by

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not covering the foot. But, because players do not impact the ball beyond the phalanges, it was

not representative of human kickers to test the most distal locations across the phalanges. For the

non-rigid ankle, the most proximal impact location that the contact area during impact did not

exceed the three-dimensionally printed foot segment was analysed. Beyond this point, the contact

area between foot and ball exceeded three-dimensionally printed foot segment. Assuming the

three-dimensionally printed material did extend up to the knee-cap to represent the surface of the

entire shank segment, impacting proximally beyond this point may continue to increase ball

velocity for a limited distance, but, ball velocity will reduce at a location because the linear

velocity of the impacting point is reducing due to moving closer to the axis of rotation (knee). For

the human kickers, players likely restricted the impact locations to a limited range on their foot.

Given the players were experienced kickers, they would have purposely reduced the impact

locations to an area that did not produce substantial pain due to hyper-plantarflexion, supported

by the relationship between proximal-distal impact location with ankle plantarflexion. Further, it

is possible they also restricted the impact locations to an area that produced an ample impact

efficiency for the task. Statistical variance in the impact locations was achieved from the

variability players produced, which is different to that by Ishii and colleagues, who used a tee

with different heights to facilitate a greater range of impact locations (Ishii, et al., 2012). Thus,

because not all impact locations were analysed with the mechanical limb and because players

restricted their impact locations to within a desired range, the full extent of proximal-distal impact

location was not analysed and thus these results do not oppose the optimal relationship between

proximal-distal impact location with impact efficiency and ball velocity. Therefore, it is suggested

that coaches should assist players in exploring the proximal-distal impact location on their foot to

determine the location that is best for the task.

10.1.1.3 Medial-lateral impact location

Ball velocity and impact efficiency were influenced minimally by medial-lateral impact

location over the range of impact locations tested. The relationship between medial-lateral impact

location with ball velocity was analysed with the mechanical kicking machine, and ball velocity

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showed little dependence on impact locations tested. Ball velocity reduced from a maximum of

25.0 m/s to a minimum of 24.5 m/s, from a location just medial from the foot centre to the most

medial impact location tested. The entire width of the foot was not analysed; however, it was

considered ball velocity would continue to reduce as impact location was moved away from the

foot centre as identified by Asai, et al. (2002). This suggests medial-lateral impact location is an

important characteristic for impact efficiency and ball velocity.

The influence of medial-lateral impact location on other impact characteristics, such as

azimuth ball flight trajectory, is likely to be far more detrimental to performance in gameplay.

For the most medial impact location tested with the mechanical kicking machine, when ball

velocity reduced from 25.0 m/s to 24.5 m/s, azimuth ball flight trajectory was -8°. For a 35 m kick

toward goal, which is a conservative distance that players will find difficult to reach whereby any

reduction in ball velocity should be avoided, the ball will land 4.9 m to the side of the goal

(assuming ball curve is not influenced). Conversely, by neglecting air resistance and using a

constant elevation angle of 35°, the reduction in ball velocity from 25.0 to 24.5 m/s will translate

to a 2.4 m reduction in kick distance. It can also be considered that if air resistance was not

neglected the ball would still reach the target, as the kick distances were 59.9 and 57.4 m,

respectively. The change to azimuth angle within the tested range is far more detrimental in

absolute distances compared to the reduction in kick distance due to velocity. In a game situation,

this would miss the goals for all football codes: the goals in Australian football are 6.4 m wide;

the goals in rugby league and union are 5.5 m and 5.6 m wide; the goals in soccer are 7.3 m wide.

Each attempt at goal under this scenario, when the player aimed for the centre of the goals, would

be unsuccessful, whereas the kick distance would still surpass 35 m. Thus, while medial-lateral

impact location likely does influence ball velocity and impact efficiency, the influence of medial-

lateral impact location has the greatest effect on kick outcome by influencing azimuth ball flight

trajectory.

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10.1.1.4 Ball orientation

Ball orientation is influential to the magnitude of energy transferred to the ball. The

mechanical kicking machine identified ball velocity and ball spin were highest at a given ball

orientation. Post-hoc analysis of these results combining both translation and rotational kinetic

energy identifies the highest kinetic energy transferred to the ball occurred at an orientation of

45° degrees in the global axis (Figure 10.1). Further post-hoc analysis of the data identifies the

foot-ball angle (calculated from the surface angle of the foot surface) was 59° (Figure 10.2A).

Interestingly, this angle is greater than that usually used by drop punt kicking but consistent with

rugby place kicking (see Figure 10.2B and Figure 5 in Nunome, et al. (2014)). Using a reduced

foot-ball angle will decrease the distance between the ball centre of mass and the impact location

on the foot, whereby any off-angled foot-ball angle Y will have less of an influence on the

resulting ball flight path. This, however, is speculation, and future research is required to

determine the how foot-ball angle influences kick outcome, not just impact efficiency, on kicking

with human players.

Figure 10.1: The relationship between ball orientation and kinetic energy (both

translational and rotational) for the mechanical kicking machine.

0

20

40

60

80

100

120

140

160

-20 0 20 40 60 80 100

Kin

etic e

ne

rgy (

J)

Ball orientation (°)

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Figure 10.2: foot-ball angle that produced highest kinetic energy for the mechanical kicking

machine (A) and the foot-ball angle commonly used in drop punt kicking (B).

10.1.1.5 Ankle stiffness

Increasing ankle stiffness increases impact efficiency. Increasing ankle stiffness was

identified to increase impact in both studies with the mechanical kicking machine, in the

comparison of non-rigid to rigid ankle and in the analysis of a non-rigid ankle. Several strategies

have been discussed within the literature to increase ankle stiffness within human kickers:

adopting a position of greater ankle plantarflexion at the beginning of foot-ball impact, increasing

the stiffness of the muscle tendon units surrounding the ankle joint, and by actively dorsiflexing

at the beginning of impact.

Adopting a position of greater ankle plantarflexion at the start of impact increases the

stiffness of the ankle as the muscle tendon unit stiffness is increased. Increasing the stiffness of

the spring in the mechanical kicking machine (replicating dorsiflexion muscle tendon unit) was

identified to reduce ankle plantarflexion and increase the effective mass of the striking limb. It is

well documented the stiffness of the human muscle tendon unit also increases when stretched

(Morse, Degens, Seynnes, Maganaris, & Jones, 2008), thus adopting a more plantarflexed

position will theoretically increase the stiffness of the ankle joint during foot-ball impact. This

strategy has previously been suggested in football kicking (Peacock, et al., 2017a; Sterzing, et al.,

2009). Post-hoc analysis of the human kickers in this study weakly supports the effectiveness of

this strategy Table 10.1; significant (p < 0.05) negative linear relationships between change in

A B

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ankle plantarflexion with plantarflexion at the beginning of impact were identified in four of the

10 players, indicating adopting a more plantarflexed position reduced change in plantarflexion

during foot-ball impact for some players. It is important to note that proximal-distal impact

location was identified as an important factor influencing change in ankle plantarflexion. To

accommodate this factor, further correlations between ankle angle at impact start and change in

ankle angle but partial to proximal-distal impact location identified a significant relationship in

two players, not four. This result suggests this strategy might not be effective. This may be

explained by players not purposely using a range of different ankle positions at impact start,

whereby the statistical power would be low for the regression. Alternatively, the previous results

(Peacock, et al., 2017a; Sterzing, et al., 2009) did not account for differences in impact location

in their statistical analysis, as performed here, and may have influenced the results, whereby this

strategy might not actually be effective. However, given the strong theoretical support of this

strategy from both the mechanical kicking machine and increasing stiffness of a stretched muscle

tendon unit (Morse, et al., 2008), future work should be performed to determine the full

effectiveness of this strategy in human kickers. This could be achieved by either generating a

range of different ankle positions at the start of impact for a given kick distance where a

correlation could be performed partial impact location, as performed here. Or, a group comparison

such as a pre- and post- intervention would also be feasible, where players are trained to increase

ankle plantarflexion at the beginning of impact.

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Table 10.1: Correlation (r) between ankle dorsiflexion angle at impact start and change in

ankle plantarflexion; correlation (r) between ankle dorsiflexion angle at impact start and

change in ankle plantarflexion partial to impact location across the proximal-distal

direction on the foot.

Correlation (r) Partial correlation (r)

P01 0.745* 0.644*

P02 -0.182 0.030

P03 -0.279 -0.093

P04 0.344* 0.486*

P05 0.139 0.109

P06 -0.276 -0.028

P07 0.414* -0.116

P08 0.241 0.054

P09 0.393* 0.147

P10 0.325 0.210

* indicates significance

The strength of an athlete is a mechanism that has been suggested to influence change in

ankle plantarflexion during foot-ball impact (Ball, et al., 2010). Resistance training has been

identified to increase both the stiffness of the tendon structure and muscle strength and size (Kubo,

Kanehisa, & Fukunaga, 2002), and thus is another possible mechanism to reduce ankle

plantarflexion during impact and increase foot-ball speed ratio. The effects of resistance training

could be two-fold. Firstly, performing resistance training on the dorsiflexion muscle tendon unit

of the ankle joint will increase their stiffness, reducing the magnitude of plantarflexion as it is

stretched during foot-ball impact. Secondly, performing resistance training on the plantarflexion

muscles of the ankle joint as well, to co-activate the plantarflexion and dorsiflexion muscle groups

to pre-stretch the muscle tendon unit of the key dorsiflexion muscle group will again increase

stiffness. Future work should investigate the efficacy of resistance training to improve stiffness

of the ankle joint and how this influences performance in football kicking.

While the stretch reflex within the dorsiflexion muscle group won’t respond to the initial

conditions at impact, it might increase the stiffness of the ankle joint as it is forced into

plantarflexion during the forward leg swing. The reflex of the ankle dorsiflexion muscle group

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was discussed previously to not be influential during foot-ball impact because the response time

was far greater than the impact duration. But, the stretch reflex mechanism might still be active

during foot-ball impact, due to the motion dependent forces applied to the foot/ ankle during the

forward leg swing. Koike and Bezodis (2017) identified two of three players produced a

dorsiflexion torque just prior to impact in the rugby place kick. Their model to calculate torque

included the motion dependent terms (centrifugal/ Coriolis forces), whereby the dorsiflexion

torque could have been provided from passive structures at the end of the plantarflexion range of

motion, the stretch reflex process, the muscular torque (which they stated), or a combination of

all factors. It was also identified in the mechanical limb during the analysis with the non-rigid

ankle that when foot velocity was increased with a constant ankle stiffness, the motion dependent

forces increased the magnitude of energy stored in the spring mechanism and released into

dorsiflexion motion just prior to impact. Thus, because an external plantarflexion torque is applied

to the ankle prior to the beginning of foot-ball impact, the stretch reflex might contribute to ankle

stiffness during foot-ball impact.

Another technique to restrict the passive response of the ankle during impact is by

actively dorsiflexing at the beginning of impact. Chapter 5 identified in the analysis of foot

velocity that dorsiflexion motion at the beginning of impact increased, restricting the change in

ankle plantarflexion in the higher foot velocities despite the greater external forces applied.

Dorsiflexing at the beginning of impact, was considered to increase impact efficiency because the

storage of energy in the spring mechanism, occurring under a plantarflexion motion, was delayed.

It was also identified by Peacock, et al. (2017a) and Shinkai, et al. (2009) that players dorsiflex

at the beginning of impact in drop punt and instep kicking. The analysis by Koike and Bezodis

(2017) does also suggest muscular force may have been applied immediately prior to impact,

possibly to actively dorsiflex leading into impact. Dorsiflexing at the beginning of impact will

compromise the ability to adopt the most plantarflexed position at the beginning of impact,

because with any dorsiflexing motion the ankle is moving away from a position of plantarflexion.

It was beyond this thesis to identify which strategy might be most effective, or if a combination

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of both strategies is best. Future work should explore the effectiveness of actively dorsiflexing at

the beginning of impact to increase impact efficiency.

The analysis of impact location for the human players identified that players targeted a

location on their foot that corresponded to a change ankle plantarflexion of less than 3°, a location

near the highest impact efficiency. The mean proximal-distal impact location for each player

yielded a change in ankle plantar/ dorsal flexion of < 3° during impact. It could not be identified

why players targeted this specific location, but it does identify that players targeted a location on

their foot that produced little-to-no change in ankle plantarflexion during foot-ball impact. This

might suggest that strategies to reduce the magnitude of ankle plantarflexion will not be effective

because there is already little-to-no change in ankle position. However, while a player might

exhibit a change in ankle plantarflexion of 0° from start to finish of foot-ball impact, this does not

indicate the ankle was completely rigid during impact as a change in ankle angle of 0° can also

be achieved by undergoing an equal magnitude of ankle plantarflexion and dorsiflexion during

impact. For example, further analysis of the ankle motion for Player 4 identified during trials that

experienced a small change in ankle plantarflexion during impact (< ± 1°), there was no linear

ankle motion from beginning to end of impact, but a combination of both plantarflexion and dorsal

flexion during impact (Figure 10.3). Under these kicks, using the total change in ankle

plantarflexion might indicate the foot was acting as a rigid body, or close to a rigid body, because

if the magnitude of dorsiflexion is equal to plantarflexion the elastic energy stored is released.

However, due to the hysteresis of the muscle tendon unit (Taylor, Dalton JR, Seaber, & Garrett

JR, 1990), the magnitude of released elastic energy would be less than the stored energy. Thus,

not all cases where the ankle undergoes a change in ankle angle of 0° is it acting like a rigid body.

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Figure 10.3: Ankle plantar/dorsal flexion of three kicks that underwent a total change in

ankle angle of less than 1°.

It is recommended players should employ strategies to reduce ankle plantarflexion for

two reasons. Firstly, when impacting at the ‘sweet spot’ for change in ankle plantarflexion along

the foot, where the change in ankle angle is 0°, it was just identified the ankle still goes through

a change in position during impact and is not completely rigid. Theoretically, increasing stiffness

of the ankle at this change in ankle plantarflexion ‘sweet spot’ may reduce the peaks and troughs

of the ankle motion during impact and increase impact efficiency (Figure 10.4, comparison

between line A and line B). Secondly, employing strategies to reduce ankle motion might increase

the ‘power zone’ on the foot, an area on the foot that produces a foot-ball speed ratio above a

certain threshold. While players targeted the location on their foot that produced minimal ankle

plantarflexion during impact, they also yielded end-point variability and impacted at a distance

from this location in some trials. Employing strategies to increase the stiffness of the ankle for

these impact locations away from the change in ankle plantarflexion ‘sweet spot’ might increase

the ‘power zone’ (Brody, 1981). Mathematically, this will decrease the quadratic coefficient of

the second order relationship between proximal-distal impact location with foot-ball speed ratio.

For example, a player might produce an area of 3 cm where foot-ball speed ratio is above 1.30,

but the area might increase to 5 cm by employing strategies to increase ankle stiffness (Figure

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 2 4 6 8 10 12

Chan

ge

in a

nkle

pla

nta

rfle

xio

n (

°)

Impact duration (ms)

Kick A

Kick B

Kick C

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10.4, line A compared to line C). This suggestion was also made by Ishii, et al. (2012), whereby

they suggested increasing the ankle joint torque assisted in increasing ball velocity at distal impact

locations. Furthermore, their model also suggested the ‘sweet spot’ was shifted distally. As a

player may be able to hold the ankle joint fixed when impacting distally which will be travelling

at a higher linear velocity, thus is beneficial to ball velocity.

Figure 10.4: Theoretical analysis of the relationship between proximal-distal impact

location and foot-ball speed ratio in response to increasing the stiffness of the muscle

tendon unit. Line A represents the untrained ankle. Line B represents an increase foot-ball

speed ratio due to reduced ankle motion during foot-ball impact. Line C represents an

increase in the ‘power zone’, whereby a stronger muscle tendon unit may allow for greater

end-point variability in impact location.

10.1.1.6 Foot velocity can increase ball velocity but decreases impact efficiency

Foot velocity can be used to increase ball velocity despite a reduction in impact

efficiency. Impact efficiency will decrease due to both a reduction in coefficient of restitution of

the ball and due to an increased external torque applied to the ankle joint. It is currently not known

if there are any strategies a player can use to negate the negative effect of increasing foot velocity

1.00

1.10

1.20

1.30

1.40

-4 -3 -2 -1 0 1 2 3 4

Fo

ot-

bal

l sp

eed

rat

io

Proximal-distal impact location (cm)

A

C

B

188

on impact efficiency, and could be a direction of future work. The influence of foot velocity on

the impact phase is still important for coaches, as they should be aware of the influence of foot

velocity on ankle motion and that impact efficiency will decrease as they kick further distances.

10.1.2 Does reducing change in ankle plantarflexion during foot-ball impact influence

impact efficiency?

Reducing the magnitude of ankle plantarflexion was suggested as an effective strategy to

increase impact efficiency. However, critical review of the literature identified no empirical

evidence supporting the strategy. Thus, the effectiveness of the coaching cue ‘maintaining a foot

firm and reducing the magnitude of ankle plantarflexion during impact’ was not known. The

following section will determine the effectiveness of reducing ankle plantarflexion to increase

ankle plantarflexion.

Ankle motion during impact is a passive response to the initial conditions at ball contact.

Nunome and colleagues (Nunome, et al., 2006b) first suggested ankle motion during impact was

passive, and the results within this thesis of both the mechanical kicking machine and the human

performers support this suggestion. The response of an ankle that is passive in nature was

identified from the mechanical kicking machine, whereby the resulting change in ankle position

during impact is influenced by the internal and external torque applied to the ankle during impact

and the pre-existing motion of the ankle. The response of the ankle for human kickers was

identified to be passive due to the similarities with the relationship between the proximal-distal

impact location and change in ankle plantar/dorsiflexion in human kickers. For both human

players and the mechanical kicking machine, a distal impact location increased the magnitude of

ankle plantarflexion because the external torque increased. Each of the human kickers produced

either perfect or near perfect relationships between proximal-distal impact location with change

in ankle plantarflexion. Thus, the ankle motion for human kickers is passive during impact and is

determined by the internal and external torque applied to the joint and the pre-existing motion of

the ankle joint.

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Ankle motion is passive due to the extremely short duration of the impact phase. The

impact phase lasts approximately 7 – 16 ms (Peacock, et al., 2017a; Shinkai, et al., 2009). The

transfer of energy from foot to ball occurs over about three fourths of the phase (Peacock, et al.,

2017a; Shinkai, et al., 2009), where any active contribution by the ankle must therefore occur

within three-fourths of impact, or 5 – 12 ms from ball contact depending on the overall contact

time. However, any active response from the ankle occurs after this time. The monosynaptic

reflex, the quickest reflex in the body, is in the range of 20 – 40 ms between individuals (Latash,

2012). But, specific research on the dorsiflexion muscle group, the muscle group that is stretched

during plantarflexion, has identified the muscle fires at 50 ms post muscle-twitch and peaks at

150 – 300 ms (Sinkjaer, Toft, Andreassen, & Hornemann, 1988). Given the force applied from

foot to ball increases over the initial period of impact (Iga, et al., 2017; Shinkai, et al., 2009) and

ankle plantarflexion typically begins at 2-3 ms post contact (Peacock, et al., 2017a; Shinkai, et

al., 2009), the muscle twitch of the dorsiflexion muscle group can be expected to occur at 2 – 3

ms post ball contact. This means the muscle will fire at 52-53 ms post ball contact, and then

increase its contribution until 153 ms post ball contact. However, the impact phase has ceased

when the contribution of ankle dorsiflexion muscle work occurs, where the ankle is passively

responding to the initial conditions at ball contact during the entire foot-ball impact phase.

It has been suggested that players might use several strategies to actively control the

resulting change in ankle position, which might suggest the ankle motion is active and not passive.

Several strategies have been identified to reduce the magnitude of ankle plantarflexion:

dorsiflexion just prior to impact (Chapter 5), increasing the magnitude of plantarflexion at the

beginning of impact (Peacock, et al., 2017a; Sterzing, et al., 2009), and increasing the muscle

stiffness (Ball, et al., 2010). It is important to differentiate between these active strategies and

passive response of the ankle. The passive response of the ankle refers to the motion of the ankle

during impact in response the initial conditions at ball contact. Active strategies are either pre-

programmed task specific strategies or are a result of feedback gained during the leg forward

swing when there is ample time to functionally adapt the execution. The initial conditions of

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impact, which the ankle passively responds to, comprises these active strategies. While players

might actively alter the conditions of the ankle at the start of impact, the ankle responds passively

during impact to these strategies and the external torque applied to the joint.

All results within this study did identify impact efficiency was largest when change in

ankle plantarflexion was minimised, supporting the coaching cue of maintaining a firm ankle

during impact. Each of the strategies that reduced ankle plantarflexion translated to increased

impact efficiency in the mechanical kicking machine: comparison of rigid to non-rigid ankle;

proximal-distal impact location; increasing ankle stiffness; and actively dorsiflexing at the

beginning of impact. These results support the strategy of reducing ankle plantarflexion to

improve impact efficiency. The results of human kicking identified that impact efficiency was

highest within a change in ankle plantar/dorsiflexion of less than 3°. The limitation of the analysis

with the mechanical kicking machine was that no change in ankle position of dorsiflexion was

created by the interventions applied, where it could not be identified if ankle plantarflexion should

continually be reduced (to produce dorsiflexion) or if there is an optimal magnitude of ankle

plantarflexion. The analysis of human kickers identified ankle dorsiflexion did occur regularly,

providing the opportunity to explore if continual reduction in plantarflexion (to produce

dorsiflexion) or if an optimal level of ankle plantarflexion is best for impact efficiency. Of the

four players that a sweet spot location could be identified on the proximal-distal direction of the

foot by foot-ball speed ratio, this impact location translated to a change in ankle plantarflexion of

< 3°. This suggested an optimal level of ankle plantarflexion was best for impact efficiency.

Further, post-hoc bivariate analysis of the human kickers identified six of ten players produced a

significant relationship directly between change in ankle plantarflexion with impact efficiency,

with all players again producing the highest impact efficiency at a change in ankle angle of < 3°

plantar/dorsiflexion. The results within this thesis identify that reducing the magnitude of ankle

plantarflexion to within a small magnitude (< ±3°) produced the highest impact efficiency.

Reducing the magnitude of ankle plantarflexion did not always increase ball velocity.

While the results in this thesis identified that reducing the magnitude of ankle plantarflexion to a

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small magnitude produced the highest impact efficiency, specifically reducing the magnitude of

ankle plantarflexion did not always increase ball velocity. Reducing the external torque applied

to the ball was identified to reduce the magnitude of ankle plantarflexion during impact. Reducing

the magnitude of foot velocity at ball contact can reduce the external torque, however, the linear

relationship between foot velocity and ball velocity indicates that any reduction to foot velocity,

while it might reduce the magnitude of ankle plantarflexion, will reduce ball velocity. Thus,

reducing ankle plantarflexion does not increase ball velocity, rather, it increases impact efficiency.

Reducing change in ankle plantarflexion did not directly influence impact efficiency

because ankle motion was passive during impact. While it was identified that restricting the

magnitude of ankle plantarflexion to within a small magnitude (< ±3°) produced the highest

impact efficiency, reducing change in ankle plantarflexion, as a theoretical construct, did not

influence impact efficiency because ankle motion was passive during impact. Players could not

solely actively reduce change in ankle plantarflexion to improve impact efficiency. Rather, they

controlled the internal/ external torque applied to the ankle or the pre-existing ankle motion at the

beginning of impact. It is the strategies that players used to alter the internal/external torque

applied to the ankle joint and/ or the pre-existing ankle motion at the beginning of impact that

influenced impact efficiency. The results within this thesis identify that increasing rigidity,

impacting closer to the ‘sweet spot’ on the foot, increasing the dorsiflexion angular velocity

immediately prior to impact, and reducing foot velocity each increased impact efficiency.

Assessing ankle motion can be used by coaches as a valid tool to provide feedback on the

quality of impact. The previous discussion on ankle motion influencing impact efficiency was

philosophical, but the practical outcomes from this work identified that assessing ankle motion

can be used as a valid tool to assess the quality of impact because impact efficiency was generally

largest when ankle plantarflexion was minimised. The highest identified impact efficiency was

greatest for the individuals with a change in ankle plantarflexion of < ± 3°, whereby coaches can

assess the ankle motion during impact to provide feedback on how they can reduce this motion to

a small magnitude. If players do display a large magnitude of ankle plantarflexion, they can reduce

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this magnitude through several strategies such as altering the impact location and increasing the

rigidity of the ankle joint. Individual strategies to increase impact efficiency are discussed in

Chapter 10.1.1 .

The mixed results on the effectiveness of reducing ankle plantarflexion in previous

literature were likely due to confounding impact characteristics. Critical review of the literature

identified mixed results on the effectiveness of reduced ankle plantarflexion to increase impact

efficiency and/ or final ball velocity. Studies discussing the issue identified reduced ankle

plantarflexion had a positive influence on impact efficiency or ball velocity (Asami & Nolte,

1983), had statistically no influence on impact efficiency or ball velocity (Ball, et al., 2010;

Nunome, et al., 2006b; Peacock, et al., 2017a; Shinkai, et al., 2013; Sterzing, et al., 2009), or they

were not original papers exploring the issue (Kellis & Katis, 2007; Lees & Nolan, 1998).

However, these analyses (excluding the literature reviews) were performed at a group level.

Individual differences in physical mass, impact location, and foot velocity each would have

influenced ankle plantarflexion, impact efficiency and ball velocity. The results from this thesis,

performed on an individual level, identified that strategies to reduce ankle plantarflexion were

beneficial to impact efficiency.

10.1.3 Limitations and future directions to increase impact efficiency

The work within this thesis identified several strategies that a player can employ to

increase impact efficiency, but future work should be performed to determine the effectiveness of

these strategies. Increasing joint stiffness, increasing the pre-existing ankle dorsiflexion motion,

or impacting the ball at the optimal impact location on the foot were each identified to increase

impact efficiency. Future work should explore how players can implement these strategies over

long term to determine their effectiveness against a control group. For example, it was identified

that increasing the stiffness of the ankle joint improved impact efficiency in the mechanical

kicking machine, and it was discussed that resistance training on the musculature around the ankle

joint might be an effective method to implement this strategy as previous work has identified

resistance training increases the muscle tendon unit stiffness. However, it was not identified if

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performing resistance training, in comparison to a control group, increases impact efficiency. This

highlights the limitation of the work within this thesis, where the theoretical aspects on impact

efficiency were identified, and future research is required to determine the effectiveness of these

strategies in comparison to a control group.

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10.2. How do foot-ball impact characteristics influence ball flight

characteristics and kicking accuracy

10.2.1 The influence of foot-ball impact characteristics on ball flight characteristics and

kicking accuracy

Ball flight trajectory and velocity, not factors associated with ball spin, were more

important ball flight components for kicking accuracy. Azimuth ball flight trajectory was

identified as the most important factor toward the horizontal component of kicking accuracy in

Chapter 8, and further analysis of this dataset identifies ball elevation angle and ball velocity were

most influential to the vertical component of the vertical plane. Theoretically, vertical component

of kicking accuracy will be influenced by ball velocity, elevation angle and spin rate. Further

multiple linear regression analysis of these three variables from the dataset analysed in Chapter 8

explained 35.4% of variance within the vertical component of kicking accuracy, whereby

elevation angle and ball velocity were most important/ influential as indicated by the standardised

coefficients (Table 10.2). The influence of ball aerodynamics, as represented by back-spin rate,

had less of an influence on the vertical component of the vertical plane, as similarly identified in

the horizontal component where azimuth ball flight trajectory was the most important variable.

These results indicate errors in kicking accuracy were more influenced by the trajectory and

velocity of the ball, and less explained by the factors associated with ball spin. This might be due

to the dynamics of the drop punt kick, where the ball ‘rolls’ up the foot. The ability to apply the

distinct back-spin might be easily to achieved as the ball rolls up the foot and rotates about its

longitudinal axis. Important to note, wind will also influence ball curve in the outside environment

but was not included in this analysis.

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Table 10.2: Multiple linear regression results predicting the vertical component of kicking

accuracy. This regression was performed using the same methods and dataset from

Chapter 8.

B σe β

Constant -5.961 1.94

Ball back-spin -0.034 0.011 -0.276

Elevation angle 0.114 0.024 0.815

Ball velocity 0.243 0.066 0.578

B = coefficient; σe = standard error of coefficient; β = standardised coefficient.

A lower magnitude of variance in the vertical component of kicking accuracy was

explained by the ball flight characteristics (35.4%) in comparison to the percentage of variance

explained by ball flight characteristics influential to the horizontal component (69.9%). Two

factors might explain why a lower variance was explained by the ball flight characteristics. Firstly,

a multiple linear regression was used to identify the influence of individual ball flight

characteristics. As the name suggests, a linear regression assumes the influence of each

independent variable in explaining the variance in the dependent variable is linear. Not all ball

flight characteristics, however, are expected to have a linear influence on the ball flight path.

Back-spin rate, for example, will influence the lift force applied to the ball during its flight and

therefore the measurement of vertical kicking accuracy. The influence of back-spin rate on the

lift force not linear, but exponential (Equation 10.1). Thus, the influence of some ball flight

characteristics on the vertical measurement of kicking accuracy might not be represented fully by

the linear regression.

𝐹𝐿 =

1

2𝐶𝐿𝜌𝐴𝑣2

Equation 10.1

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Where FL = lift force; CL = dimensionless lift coefficient; 𝜌 = air density; A = cross-

sectional frontal area; v = velocity.

Secondly, the unexplained variance might be due to the measurement of the vertical

component of kicking accuracy, which was susceptible to a larger magnitude of error compared

to the horizontal component. If the receiving player moved off the 30m line when catching the

ball, an error in the measurement occurred because the catch position and the true position of the

ball passing through the 30m plane are not equal due to the downward trajectory of the ball toward

the ground. While the videos were screened to eliminate kicks where the ball fell short of or

travelled overhead of the receiving player, it is possible the ball was caught where the receiving

player moved a small distance (< 0.5 m) off the 30 m plane. Due to the downward trajectory of

the ball just prior to being caught, the measurement of kicking accuracy will be understated as the

receiving player moves toward the kicker, and the measurement of kicking accuracy will be

overstated as the receiving player moves away from the kicker. A quantitative error analysis could

not have been performed because the three-dimensional vector of the ball was not recorded at and

immediately prior to being caught, however a two-dimensional analysis of one kick identified the

horizontal ball speed was 0.8 m/s and the vertical speed was 13.0 m/s over the final two frames

prior to being caught for a kick that was off-target. If, hypothetically, the ball was travelling at an

angle of 50° from the horizontal, the ball would be travelling at 10.9 m/s toward the target. As

can be seen in the Figure 2 of Goff (2013), the ball arrives to the ground with a greater elevation

angle than the take-off angle due to the lift and drag forces applied to the ball during flight, thus

this 50° approximation is ample for this analysis given the take-off elevation angle of the kick

was measured 19.0°. If the player catching the ball moved 0.5 m off the 30 m plane of the kick

distance toward the kicker, the ball would be caught 0.05 seconds earlier, producing an error of

0.004 m in the horizontal component and 0.65 m in the vertical component. This larger magnitude

of error in the vertical component might explain why a larger percentage of variance was

unexplained by ball flight characteristics. While multiple linear regression can identify the

influence of several independent variables on one dependent variable, future research exploring

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the ball flight characteristics influencing the vertical component of kicking accuracy should

develop employ a method capable of detecting non-linear influence of parameters and use a

measurement that is less susceptible to error.

Foot elevation angle was an important factor influencing ball elevation angle in human

kickers. To get an indication of the impact characteristics that influence the vertical component

of kicking accuracy, an additional multiple linear regression was performed to identify the

variability in foot-ball impact characteristics that influenced ball elevation angle. Ball velocity

was identified as the second most important factor, and an analysis of factors that influence ball

velocity have been discussed heavily in this thesis and will not be discussed again in this section.

Understanding what factors influence ball elevation angle is a new analysis to progress the

understanding of kicking accuracy in human kickers. Foot velocity, foot-ball angle about the X

axis, and proximal-distal impact location were identified to have substantial influences on

elevation angle in the mechanical kicking machine (Chapter 4). Therefore, to get an indication of

the variability that players produce in their impact characteristics and how it relates to vertical

kicking accuracy, a multiple linear regression analysis was performed to identify the dependence

of ball flight elevation angle on foot velocity, foot-ball angle X and foot elevation angle for two

players. Because the ankle was rigid in this analysis with the mechanical kicking machine, the

influence of proximal-distal impact location was not representative of human kickers and was not

included in this analysis. Foot elevation trajectory was included in the regression analysis because

it was discussed as being influential in the analysis within the mechanical kicking machine despite

not systematically analysed, and because players are able to vary foot elevation angle between

kicks. The regression results indicated that foot elevation trajectory was the only predictor for

both players, and explained 79.1% and 84.2% of the variance (Player 4; Player 6). Given the clear

results for both players, whereby foot elevation trajectory explained such a large portion of

variance, it was warranted to perform a bivariate analysis for all players between these two

variables. This analysis identified a similar result: foot elevation trajectory was a significant

predictor for all individuals, with 9 of 10 players displaying either a perfect or near perfect linear

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relationships and the remaining player producing a second order relationship (Table 10.3). This

result identifies the foot trajectory was an important factor for ball elevation angle, and therefore

an important factor influential to the vertical component of kicking accuracy.

Table 10.3: Bivariate regressions of the relationship between foot elevation trajectory and

ball elevation angle.

Player Relationship R-value p-value Effect classification

1 Linear 0.76 <0.01 Nearly Perfect


3 Linear 0.85 <0.01 Perfect




7 Second order 0.54 0.01 Nearly Perfect




Expanding the oblique impact theory to the entire duration of impact provided a

theoretical basis to describe the interaction between foot-ball impact with ball flight

characteristics. The oblique impact theory was used to describe the relationship between foot-ball

impact characteristics with ball flight characteristics in the mechanical kicking machine and

human kickers. The limitation of this theory is that it assumes the collision between two objects

occurs instantly, whereas the collision between foot and ball during impact occurs over a time of

approximately 10-12 ms as the ball deforms over the foot. Given it was previously identified the

transfer of energy from foot and ball occurs over three fourths of impact duration (Peacock, et al.,

2017a; Shinkai, et al., 2009), the formation of ball flight characteristics was logically expected to

also occur over this time period and not instantaneously at the beginning of impact. Supporting

this was the analysis within Chapter 9 of a non-uniform increase in ball angular velocity through

impact, similar to that found by Shinkai, et al. (2009) with sagittal plane ball velocity. Thus, the

oblique impact theory applied to the duration of impact describes how the combination of flight

characteristics are determined.

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The oblique impact theory indicates ball flight characteristics are influenced by the

surface angle of the contact area between foot and ball and the foot-ball angle. The results within

this thesis identified the application of the oblique impact theory to the duration of impact

provided a theoretical framework to explain why individual impact characteristics influence ball

flight characteristics. There are three components to the oblique impact theory that explain how

ball flight characteristics are influenced. Firstly, the surface angle between the foot and ball will

influence the direction of the force vector applied to the ball. Impact locations that are off-centre

across the medial-lateral direction, where the perpendicular direction of the surface angle does

not point toward the target, will alter the direction of the force vector to the perpendicular direction

of the surface angle. For example, the surface angle of the impact location on the lateral aspect of

the foot points laterally to the target, where the force vector is applied in the lateral direction.

Secondly, the force vector applied to the ball may produce a torque, where a component of that

force vector is producing rotational energy at the expense of translational energy. For an

ellipsoidal or any non-spherical ball, the foot-ball angle is an important component to the torque.

Thirdly, energy is continually transferred from foot to ball as the ball deforms over the foot during

impact, whereby the dynamic nature of impact influences the outcome. As the ball deforms over

the foot and the contact area moves, the direction of the force vector applied from foot to ball and

the torque applied to the ball will change.

Foot-ball impact characteristics influenced kicking accuracy. This thesis explored how

foot-ball impact characteristics influenced kicking accuracy through two steps. Firstly, the

relationship between impact characteristics with ball flight characteristics was identified with the

mechanical kicking machine and human kickers. The key result of this analysis was that changes

to each impact characteristic influenced ball flight characteristics, as explained by the oblique

impact theory applied to the duration of impact. Secondly, the relationship between ball flight

characteristics and a measurement of kicking accuracy was identified, where it was found ball

flight characteristics influenced kicking accuracy. The culmination of this work identified that

foot-ball impact characteristics influenced kicking accuracy. Important to note, however, foot-

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ball impact characteristics will not always influence kicking accuracy due to the adaptive

variability that exists within both foot-ball impact and ball flight characteristics. Because the ball

must first travel on its flight path before reaching the target, a player can kick to a constant target

by (1) impacting the ball with a different combination of impact characteristics to produce

constant ball flight characteristics, or (2) impacting the ball with a different combination of ball

flight characteristics to produce a different combination of ball flight characteristics that will reach

a constant target. Thus, it is possible that future work may identify an instance where a constant

measurement of kicking accuracy is attained by different combinations of impact characteristics.

In plainer terms, two different measurements of kicking accuracy must be attained by two

different combinations of impact characteristics (neglecting external environment such as wind),

but two different combinations of impact characteristics will not always produce two different

measurements of kicking accuracy due to adaptive variability.

The work in this thesis has covered all aspects of kicking accuracy in gameplay, either

directly or indirectly. In gameplay, a kick is deemed successful if it reaches its desired target. In

Australian football, a successful shot at goal occurs when the ball travels within the horizontal

distance separated by the goal posts. In soccer, a successful shot at goal occurs when the ball

travels both within the horizontal distance separated by the upright posts, but also underneath the

crossbar. In the rugby codes (league, union and American football), the ball must travel over the

cross bar and within the horizontal posts. Thus, to score goals across each football code, a player

must ensure the ball passes through a vertical plane at a set distance that has horizontal constraints

and in some codes specific vertical constraints (under/ over the crossbar). A successful attempt at

passing can be considered far more advanced because the constraints in both the horizontal and

vertical planes are often large: the team member receiving the ball can only move a set distance

during the ball flight to receive any off-target ball; the kicker must ensure the ball is not

intercepted from opposition; and, the ball must not cross the boundary of the field. The direct

measurement of kicking accuracy within this thesis was made solely in the vertical plane for a

submaximal distance, where it was identified variability in the ball velocity vector (comprising

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the velocity, elevation angle and azimuth angle) explained most of the variance in the

measurement of accuracy. However, the factors influential to the measurement of accuracy in the

horizontal plane were covered indirectly. In the horizontal plane, the perpendicular distance to

the kick direction is synonymously governed by the same factors that influence the horizontal

component of the vertical plane. While the magnitudes of each variable will differ, the effective

kick distance, will also be governed by the factors influential to the vertical component of the

vertical plane as indicated by Goff (2013). Thus, all aspects of kicking accuracy have been

addressed within this thesis.

10.2.2 Why players produce inaccurate kicks: a new theory defining human kicking

accuracy

The oblique impact theory identifies the combination of impact characteristics will

influence kicking accuracy. Theoretically, all players should be able to successfully kick toward

a submaximal target. But, players do not always kick directly toward their target. Rather, they

produce inaccurate kicks, as identified within this thesis and by Dichiera, et al. (2006). This

following section will discuss why players produce inaccurate kicks.

Players cannot respond and functionally vary foot-ball impact characteristics to mitigate

errors introduced at ball contact. The results of this thesis identified that players who produced

less variability in the performance measure (azimuth ball flight trajectory) produced less

variability in their impact characteristics (ball impact location and foot-ball angle). This indicated

that players produced more consistent outcomes by varying their impact characteristics less. This

is due to the extremely short duration of the impact phase where the foot moves passively: a player

is unable to receive feedback during impact and make corrective changes to their technique to

ensure the task constraints are satisfied. Because a player is unable to make corrective changes

during foot-ball impact, they must impact the ball with a correct combination of impact

characteristics to satisfy the task constraints. Further, this indicates the ability to detect errors and

functionally vary the movement pattern does not occur during impact. Future work is required to

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understand how and where players detect and functionally vary their movement pattern during

the kick to mitigate errors within the kick.

Players can express adaptive variability in foot-ball impact characteristics to satisfy

different task constraints. The inter-individual variability indicated that each player used a unique

combination of impact characteristics to satisfy the task constraints imposed in the analysed study.

The variability in these impact characteristics between players was not random, but could be

explained by the oblique impact theory. It was identified players used a trade-off between the

impact location on the ball with a different foot-ball angle. This indicates that players can use

variability to adapt to different task constraints, but does not identify that players do. However,

theoretically, players must use a different combination of impact characteristics to generate a

different flight path required to complete a different task with changing constraints. This thesis

did not explore how players functionally vary impact characteristics to suffice differing task

constraints. However, one player did alter their approach for an additional kick (after they

completed their 30 required kicks), providing an insight into how players might functionally vary

impact characteristics. A comparison of this one kick with an angled approach, whereby the player

approached the kicking area with a lateral trajectory, to their straight approach kicks indicates

players do functionally alter their impact characteristics. Specifically, to combat the angled

approach, evidenced by a lateral ball velocity and lateral azimuth foot trajectory prior to impact,

the player used a lateral azimuth ball impact location to still maintain a consistent azimuth ball

flight trajectory (Table 10.4). This functional change in foot-ball impact characteristics by the

player is supported by the theory identified within the present thesis, whereby the lateral ball

impact location will counteract the lateral foot trajectory. Thus, players must express functional

variability in impact characteristics to satisfy different task constraints, but future work should

explore the strategies used by the players.

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Table 10.4: Comparisons of foot-ball impact characteristics from kicks with different task

constraints; indicating how players might functionally vary to satisfy different task

constraints.

M-L ball

velocity (m/s)

Azimuth foot

trajectory (°)

Azimuth ball impact

location (°)

Azimuth ball flight

trajectory (°)

Straight

approach

(N = 30)

0.3 2.1 0.6 0.2

Angled

approach

(N = 1)

1.1 9.2 8.4 -0.8

The work within this thesis provides a new theory of how kicking accuracy is attained:

variability in the combination of foot-ball impact characteristics. Kicking accuracy is attained by

impacting the ball with an appropriate combination of impact characteristics that will satisfy the

task constraints. The oblique impact theory applied through the duration of impact provides a

theoretical basis of how impact characteristics determine the ball flight characteristics. A player

can functionally vary the combination of impact characteristics to produce stable ball flight

characteristics, but, a player cannot detect errors within impact and functionally vary their impact

characteristics to mitigate these errors due to the short phase. To kick accurately, a player must

impart an appropriate combination of flight characteristics. As errors are introduced into these

impact characteristics, the outcome of the task is affected. The effect of these errors may or may

not produce an unsuccessful outcome: if the margin of error in the outcome of the task (i.e. error

in the execution) is within the boundaries of the target area (i.e. goal post width), then the task

will still be successful despite these errors.

This theory builds upon what Hennig and colleagues (Hennig, 2011, 2014; Hennig &

Althoff, 2018; Hennig & Sterzing, 2010) stated as the primary mechanism of kicking accuracy.

Hennig and colleagues stated the primary factor influencing kicking accuracy is the homogeneity

of the pressure across the dorsal aspect of the foot during impact (Hennig, 2011, 2014; Hennig &

Althoff, 2018; Hennig & Sterzing, 2010). Hennig, et al. (2009) explored the pressure distribution

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on the foot over kicks for two footwear designs, and stated that the pressure distribution,

individualised to each footwear design, was the primary factor influencing kicking accuracy.

However, between kicks within each footwear design, the outcome differs. This was identified in

the analysis within the present thesis. It can be considered that the pressure distribution across the

anterior aspect of the foot will be consistent when a player consecutively performs a kick, because

the same foot and footwear are used. But, between these executions of the kick, when the pressure

distribution on the foot will be consistent, the outcome of the task differed. This theory of the

pressure distribution for a given footwear and foot cannot explain all aspects of kicking accuracy,

and thus cannot be a primary factor of kicking accuracy. The theory in this thesis builds upon the

work of Hennig and colleagues. Accurate kicking is attained by players using an appropriate

combination of impact characteristics that will enable the ball to travel on a necessary flight path

to reach the target. Players produce variability between kicks creating a different combination of

ball flight characteristics, which may or may not produce variability in the outcome of the task.

Hennig and colleagues identified the pressure distribution was an important factor toward kicking

accuracy (Hennig, 2011). The results from this work do not oppose this finding: having a more

consistent pressure distribution across the foot surface will ensure that despite the variability a

player produces, there will be less effect on the ball flight characteristics. The pressure distribution

by itself, however, cannot explain all aspects of kicking accuracy, but is one component. The

overall components of kicking accuracy comprise the combination of ball flight characteristics to

suit the task constraints (comprising functional variability and the pressure distribution), and the

errors that players produce in the combination of ball flight characteristics relative the outcome

of the task within game (i.e. ensuring the ball travels within the goal posts, not exactly in the

middle of the goal posts).

10.2.3 Strategies to improve kicking accuracy

Reducing the magnitude of variability at foot-ball impact characteristics was identified to

reduce performance variability. The players that produced less variability in their ball flight

characteristics produced less variability in their impact characteristics. Therefore, to reduce

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performance variability, players should produce less error in their impact characteristics. The

ability to detect and mitigate errors throughout the execution of the kick prior to impact should

be learned. Future work identifying how players detect and mitigate errors should be performed.

Functionally varying impact characteristics is required to satisfy different task

constraints. To successfully perform a range of different kicks, players must impact the ball with

a different combination of impact characteristics. Thus, learning how to functionally vary impact

characteristics is important for players to kick under different conditions. The results from testing

the human kickers identified that for a constant task, players used a singular mode of execution

whereby more consistent performance was achieved through refinement of the singular execution

to reduce errors. This suggests that to learn how to functionally vary the combination of impact

characteristics, players should not repeat a task of consistent constraints because they will not

explore alternate combinations of impact characteristics. There is a large body of literature and

knowledge that has explored motor skill learning, and will not be addressed here.

Players should use a combination of impact characteristics that produce a stable outcome

of the task within the range of variability produced. The results within this thesis indicate that all

players produced variability, and the more consistent performing players produced less

variability. In gameplay, while it might appear a player produces stable outcomes (i.e. all shots at

goal being successful), these results indicate they will still produce a small magnitude of

variability, but this variability is within the range of successful completion of the task (i.e. the

range of outcomes might be within 1 m, but the width of the goals are 1.2 m). Thus, non-functional

variability will likely never be removed from a player’s movement pattern. Because players

produce variability in their impact characteristics, they should employ a combination of impact

characteristics that produces stable outcomes despite this variability. These regions of stability

can be identified from the relationships of each individual impact characteristic and ball flight

characteristics, whereby future analysis should create explicit mathematical models to further

explore this method. Two examples will be provided below: the foot-ball angle and the footwear

design.

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Players might not use the foot-ball angle of maximum impact efficiency to provide

stability in elevation angle. Given the strong dependence of ball elevation angle on foot-ball angle

X as identified with the mechanical limb (Chapter 4.3. ), it was expected foot-ball angle X to be

more influential to ball elevation angle than identified by the multiple linear regression in the

human kickers due to the variability they would produce. The results from the mechanical kicking

machine identified that ball elevation angle and back-spin rate were quite stable between the

absolute ball orientation range of 15 - 40° as this is the peak of the sine-wave that was fitted to

the relationship. This absolute ball orientation corresponds to a foot surface-ball angle between

the range of 30-65°. Previously (Chapter 10.1.1.4 Ball orientation), it was discussed that players

performing the drop punt kick did not use a foot-ball angle that transferred the highest magnitude

of kinetic energy from foot to ball. Rather, an anecdotal observation suggested players use a

smaller angle. The stability of elevation angle on foot surface-ball angle in the range of 30-65°

might explain why players don’t use the foot-ball angle that produces a higher transfer of kinetic

energy. It is possible that player use a foot-ball angle within the range of stability over the foot-

ball angle producing highest ball velocity to accommodate for the variability they produce

between their executions. Further post-hoc analysis identifies the mean foot-ball angle used by

players was 21 - 33° between players, which is not far from the range of 30 - 65° that provided

stability in the mechanical kicking machine. Differences did exist in the method of calculating

these parameters: the foot surface-ball angle and foot-ball angle are different. Differences will

also exist between players in the foot surface angle and the measurement of foot angle. Further,

the influence of foot trajectory will also influence the effective surface angle of the foot applied

to the ball. Regardless, the analysis of foot-ball angle X with the mechanical kicking machine

identifies that regions of stable outcomes exist within a range of impact characteristics. Future

work to create mathematical models that predict the outcome in three-dimensional space is

required to fully explore and identify these regions of stability.

Footwear designs that contain a constant surface angle across the range of impact

locations on the foot will theoretically produce stable ball flight characteristics. Changes to impact

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location across the medial-lateral direction directly influenced azimuth ball flight trajectory due

to the change in the surface angle across this dimension. The players that produced the least

variability in the ball flight characteristics produced the least variability in the impact location,

indicating reductions to variability will reduce performance variability for the task. However, in

addition to reducing this variability, reducing the change in the surface angle of the foot surface

will mechanically reduce the influence of this variability on the outcome of the task. Altering the

footwear designs so the surface angle is constant within the range of impact locations used due to

variability will theoretically be beneficial to producing stable ball flight characteristics. This

mechanism has been suggested before (Nunome, et al., 2014). A similar mechanism was tested

by Hennig and colleagues (Hennig, et al., 2009) where they added padding to the foot, however,

they identified no statistically significant differences in performance. Further exploration is

warranted due to the limited approach taken. This footwear design might come at the expense of

the ability to functionally vary the impact location on the foot, which was identified as a

mechanism to satisfy different task constraints. Thus, future work is required to understand how

players functionally vary to different task constraints and design footwear to supplement the

strategies used by players. Alternatively, given the execution of a skill is influenced by the task

constraints (Davids, 2010), a player might use a different strategy to satisfy different task

constraints if there is no change to the surface angle on the foot. Future work should explore the

area of footwear designs to improve all-round kicking performance.

10.2.4 Limitations and future directions to improve kicking accuracy

Exploring the relationship between ball flight characteristics and kicking accuracy using

models should be performed. A linear regression was performed to identify the ball flight

characteristics that influenced kicking accuracy. However, as previously discussed, several flight

characteristics are known to have a non-linear influence on the flight path. Thus, more work is

required to explore the ball flight path of the ellipsoidal ball and kicking accuracy are related.

Further exploration of the stable regions of impact characteristics is required to determine

the effectiveness of this strategy. Identifying regions of stability in impact characteristics where

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the range of variability produced by the player has a little influence on the outcome of the task is

theoretically hypothesised to benefit performance. The limitation of the examples explored thus

far for this method, foot-ball angle and footwear design, was that they were based on either a

bivariate analysis or a theoretical idea. The creation of mathematical models representing the

interaction in three-dimensional space comprising several key variables – foot trajectory, foot

surface properties, ball shape – will identify these regions of stability when a larger number of

variables are included. Further, combining models of both ball flight and impact can enable a

holistic approach to identify the stable regions. Stable regions were discussed within foot-ball

impact characteristics, and it is possible they might also exist within the ball flight characteristics

and the flight path. Increasing the likelihood of kicking success could be achieved by aligning the

stable regions for impact and ball flight characteristics. Using a similar approach to that of the

present thesis, combining a theoretical and applied experimental design, will provide a strong

foundation for this analysis. For example, developing a model for one individual player based off

experimental data, identifying the stable regions, and applying corrective changes to the

individual and re-testing to determine the effectiveness of this strategy. Similarly, exploring the

foot-ball interaction can be manipulated to produce or increase these stable regions is an exciting

future direction. Producing footwear designs that have little change in the surface angle are

theoretically hypothesised to improve performance.

Identifying how players functionally vary their technique to satisfy different task

constraints and mitigate errors introduced in the execution is important for understanding kicking

performance under different contexts. Understanding how and where players functionally vary

their technique execution is an important future direction, whereby this knowledge could be used

to develop coaching cues. Further, this knowledge could also be used to understand how footwear

designs can be optimised for an individual. Creating footwear designs that increase stable regions

was discussed as a method to improve performance. However, understanding how players

functionally vary their impact characteristics when wearing both traditional footwear designs and

the footwear designs with flat surfaces is important in exploring the effectiveness of this strategy.

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10.3. Differences between mechanical kicking machine and the human

kicking limb

10.3.1 Impact characteristics of the mechanical kicking machine and the human kicking

limb

The relationship between foot-ball impact characteristics with ball flight characteristics

was explored through both the mechanical kicking machine and human kickers, setting this thesis

up to identify components of the relationship free from confounding impact characteristics. To

explore the relationship with the mechanical kicking machine, a systematic exploration of

individual impact characteristics was performed and bivariate regressions identified the type of

relationship. To explore the relationship in human kickers, ten players performed 30 kicks

providing between 20 – 30 kicks within each player for both bivariate and multiple linear

regression analyses. The combination of both experimental and statistical designs set this thesis

up to identify robust relationships between foot-ball impact characteristics with ball flight

characteristics. The influence of confounding impact characteristics was highlighted within the

literature review in this thesis, in the discussion on ankle motion most notably. While confounding

impact characteristics have not previously been identified as a key issue influencing the

relationship between foot-ball impact characteristics with kicking accuracy, this experimental

design, of both systematic exploration and intra-individual analysis, immediately eliminated,

controlled for, and reduced the number of confounding impact characteristics. Thus, the work

within this thesis has likely reduced the number of studies that produce incorrect conclusions due

to this issue of confounding impact characteristics, as identified with ankle motion, and can be

used as a foundation for future research.

Consistency in some aspects of the relationship between foot-ball impact with ball flight

characteristics was identified between the mechanical kicking machine and human kickers. Most

representative to highlight the consistency of the relationships is the direction of the coefficients

for the relationship between both medial-lateral impact location on the foot and azimuth ball

impact location with azimuth ball flight trajectory (Table 10.5). From the bivariate regression

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analysis, positive slopes were identified between all players and the mechanical kicking for the

relationship between medial-lateral impact location with azimuth ball flight trajectory, indicating

lateral impact locations translated to lateral azimuth ball flight trajectories. From the multiple

linear regression, consistent results were also identified between players with each player

displaying a negative slope. While negative slopes for the multiple linear regression might

represent the opposite pattern to the bivariate regression, this was due to a different parameter

used – azimuth ball impact location rather than medial-lateral impact location on the foot –

whereby a medial azimuth ball impact location translates to a lateral impact location on the foot.

Thus, the negative slopes of the multiple linear regressions indicate consistent direction of slopes

for both human kickers and the mechanical kicking limb.

Table 10.5: Numerical representation of relationship between medial-lateral impact

location with azimuth ball flight trajectory and the relationship between azimuth ball

impact location with azimuth ball flight trajectory.

M-L impact location with

azimuth ball flight angle

Azimuth ball impact location with

azimuth ball flight trajectory

Mechanical

kicking machine y = 27x + 7 N/A

P01 y = 13x + 8 y = -0.54x + …

P02 y = 13x + 8 y = -0.79x + ...

P03 y = 8x + 3 y = -1.08x + …

P04 y = 10x + 7 y = -0.70x + …

P05 y = 10x + 13 y = -0.76x + …

P06 y = 6x + 10 y = -0.71x + …

P07 y = 6x + 4 y = -1.13x + …

P08 y = 7x + 2 y = -0.84x + …

P09 y = 7x + 10 y = -0.76x + …

P10 y = 5x - 1 y = -0.90x + ...

Where y = azimuth ball flight trajectory; x = medial-lateral impact location/ azimuth ball

impact location, respectively.

Differences existed in the magnitudes of the slopes and in both the direction and

magnitudes of the intercepts. As identified in Table 10.5, differences existed between each player

and between the human kickers and the mechanical kicking machine in the magnitude of the slope

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and the intercepts. These differences might suggest inconsistent relationships were identified

across these comparisons, questioning the validity of the conclusions drawn. However, these

inconsistencies can be explained by two factors: individual differences in technique and foot

shape, and random statistical variance from variability in other impact characteristics. This thesis

identified the surface angle of the contact area between foot and ball influences ball flight

characteristics. Differences in the combination of impact characteristics used and the foot shape

of each player will influence the surface angle of the contact area between foot and ball across

between each trial, and will be expressed as different coefficients in the bivariate regressions due

to a different variance in the independent and dependent variables. For example, a player with a

narrow foot, where the total change in the normal direction of the foot surface angle occurs over

a smaller linear distance (Figure 10.5), is expected to produce a higher coefficient for slope

because a greater change in azimuth ball flight trajectory occurs over a shorter distance. A

different combination of impact characteristics, such as a systematic negative tilt in foot-ball angle

Y, where the contact area spreads medially from the impact location at the beginning of impact,

will require a more lateral impact location at the beginning of impact to ensure the overall contact

area is maintained, again influencing the relationship between impact location with ball flight

trajectory. Because variability in other impact characteristics – such as foot-ball angle Y – can

also influence azimuth ball flight trajectory, the coefficients in the regression can again be

influenced by this variability. Thus, differences in the magnitude of the coefficient for the slope

and the intercept can be explained by factors associated with an individual (foot shape) and the

variability they produce in foot-ball impact characteristics.

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Figure 10.5: A greater slope is anticipated for a narrower foot, because the change in

surface angle occurs over a shorter linear distance.

Another notable difference between the mechanical kicking machine and the human limb

is the design of the ankle joint. The ankle plantar/dorsal flexion motion was identified to validly

replicate that of human kickers, whereby the consistencies between the mechanical kicking

machine and the human kickers in the relationship between proximal-distal impact location and

ankle plantarflexion further cements the validity of this motion. The human ankle joint, however,

also contains ankle abduction/ adduction and inversion/ eversion. The role of three-dimensional

ankle motion was not included within this thesis, but was explored by the author. It was identified

that ankle inversion/ eversion correlated highly with azimuth ball flight trajectory (Peacock, Ball,

& Taylor, 2017b). This indicates that kicks off-centre were characterised by a large magnitude of

ankle displacement. But, as discussed previously, ankle motion is not an independent variable

during foot-ball impact, and that is why this additional analysis was not included in the

experimental chapters. Rather, the correlation between ankle inversion/ eversion with azimuth

ball flight trajectory was due to off-centre impact location on the foot. As identified with the

changes in proximal-distal impact location with ankle plantarflexion, an impact location away

Surface angle

Change in surface angle

Foot width Foot width

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from the ankle joint produces a torque forcing the ankle to change its angle. This also occurs

across the medial-lateral direction, with off-centred impact locations producing a change to ankle

inversion/ eversion. This is also evident in soccer kicking: Shinkai, et al. (2009) identified distinct

ankle abduction and eversion due to the impact location occurring slightly medially of the foot in

the instep kick. While ankle motion itself is not the independent variable influencing azimuth ball

flight trajectory, increasing the strength to prevent the change in ankle angle with off-centre

impact locations theoretically will help reduce the change in azimuth ball flight trajectory. As

identified with the mechanical kicking machine, increasing the stiffness of the dorsiflexion spring

reduced the magnitude of ankle plantarflexion. A similar mechanism is expected to occur across

the medial-lateral direction, whereby strengthening the ankle might help reduce the change in

ankle angle during impact of off-centred impacts. As the ankle is forced into inversion/ eversion,

the surface angle on the foot points further away from the target. This change in surface angle

compounds the influence of the poor impact location on azimuth ball flight trajectory. Reducing

this magnitude of ankle inversion/ eversion is expected to reduce the effect of a poor impact

location, by reducing the change in surface angle of the ankle as it changes its orientation during

impact. Future work should perform a prospective intervention study to identify the effectiveness

of strengthening the ankle joint to improve accuracy and ball velocity in human kickers.

Energy transfer mechanisms also differed between the kicking machine and human

players. In the mechanical kicking machine, it was observed that coefficient of restitution

decreased with distal impact locations and effective mass remained constant. For the human limb,

distal impact locations were observed to influence both effective mass and coefficient of

restitution. This difference was likely due to the design of the mechanical kicking machine: the

rigid foot segment and simple ankle configuration. The influence of the non-rigid properties of

the human foot with different impact locations was not assessed in the mechanical kicking

machine, and may have influenced these results. As the foot undergoes deformation the effective

mass of the striking limb may also be influenced. The ankle joint of the mechanical kicking

machine, characterised by energy stored in the spring mechanism with any magnitude of ankle

214

plantarflexion, is not entirely representative of the human ankle. While energy can be stored in

the human muscle tendon unit when it is stretched (Morse, et al., 2008), as similarly observed in

the mechanical spring, the human muscle tendon unit can also increase its length without elastic

energy being stored. As the human ankle underwent plantarflexion with distal impact locations,

it is possible the muscle component of the muscle tendon unit increased its length without elastic

energy being stored. This mechanism might influence the effective mass of the limb and not the

coefficient of restitution, because elastic energy is not being stored. These different designs of the

ankle joint and foot segment between the mechanical and human limbs might explain the observed

differences in energy transfer mechanisms. Despite these differences, consistent findings from

both experimental designs were observed for foot-ball speed ratio, a more holistic measurement

of impact efficiency comprising both effective mass and coefficient of restitution. The consistent

finding was that proximal-distal impact location influenced impact efficiency.

10.3.2 Smoothing procedures for the mechanical kicking machine and the human kickers

Different smoothing procedures were used throughout the experimental chapters despite

a constant frame rate (4,000 Hz). A low-pass Butterworth filter was applied for all chapters, but

the cut-off frequency differed. The cut-off frequency for Chapters 3, 4 and 9 was 280 Hz (kicking

machine). The cut-off frequency for Chapters 5 and 6 was 170 Hz (kicking machine). The cut-off

frequency for Chapters 7 and 8 (human kickers) was 280 Hz. Previous work exploring foot-ball

impact of Australian football kicking used a cut-off frequency of 280 Hz for sagittal plane data

captured at 4,000 Hz (Peacock, et al., 2017a). The majority of chapters used the cut-off frequency

similar to that of previous work (Peacock, et al., 2017a), at 280 Hz. The smoothing used for

Chapters 5 and 6 were a point of difference. The different cut-off frequency was due to the results

of the discrete Fourier Transform analysis looking at different cut-offs between 10 to 400 Hz and

visual inspection of the signals at different cut-offs. Less magnitude of signal was evident above

170 Hz, and this difference might be due to the design of the kicking limb. Possible design features

responsible for this difference might include the spring-controlled ankle motion. Despite this

difference, other studies exploring foot-ball impact but in soccer kicking have used cut-offs of

215

200 Hz (Nunome, et al., 2006b; Tsaousidis & Zatsiorsky, 1996), so the chosen cut-off of 170 Hz

is not an anomaly compared to other studies investigating foot-ball impact and the data were not

oversmoothed.

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10.4. Transfer of knowledge between kicking styles

Although the work in this thesis was performed solely with an Australian football ball,

there are no results within this thesis that indicate the theory identified about energy transfer and

kicking accuracy cannot be transferred to other kicking codes. While the dynamics differ between

drop punt, place kicking and soccer kicking due to different ball shapes, and approaches, these

dynamics are not anticipated to influence the transfer of this theory to other kicking types. Some

key results identified, such as variability in foot-ball angle, cannot influence kicking with a

spherical ball, but foot angle is still expected to be important. The key findings of this thesis are

(1) ankle plantarflexion does not directly influence impact efficiency; (2) the oblique impact

theory applied through the duration of impact validly explained the relationship between impact

and ball flight characteristics; and (3) players produce variability in their impact characteristics.

There are no results in this thesis that suggest these findings cannot be transferred to other kicking

codes.

217

Chapter 11: Conclusion

This thesis explored the relationship between foot-ball impact characteristics with ball

flight characteristics and kick outcome. The aims of this thesis were to (1) determine how foot-

ball impact characteristics influence impact efficiency measures (foot-ball speed ratio, coefficient

of restitution, and effective mass) and ankle plantarflexion, and (2) determine how foot-ball

impact characteristics influence ball flight characteristics and kicking accuracy. Two

methodologies were specifically chosen to answer these aims: using a mechanical kicking

machine to perform a systematic exploration of impact characteristics and an intra-individual

analysis of human kickers. These methodologies reduced the influence of confounding impact

characteristics, a key issue that has influenced the analysis of foot-ball impact in the past. The

general finding of this thesis is that foot-ball impact characteristics influenced impact efficiency

and kicking accuracy.

Impact characteristics influenced impact efficiency and ankle plantarflexion. Players can

increase impact efficiency and reduce the magnitude of ankle plantarflexion during foot-ball

impact by altering their impact characteristics. Specifically, increasing the ankle joint stiffness,

impacting closer toward the ankle joint, reducing foot velocity and altering foot-ball angle were

each identified to increase impact efficiency or energy transfer from foot to ball. The results in

this thesis generally supported the strategy of reducing the magnitude of ankle plantarflexion to

increase impact efficiency as an effective coaching cue. All results from the mechanical kicking

machine identified that reducing ankle plantarflexion through the various strategies increased

impact efficiency. The results from the human kickers were also favourable to the strategy, as

evidenced by the highest level of impact efficiency being associated with a change in ankle

plantarflexion of < ±3°. These results support the coaching cue ‘maintaining a firm ankle’ during

impact as being effective. But, philosophically, it was argued that because ankle motion was

passive during impact, due to the extremely short duration of the phase, players did not actively

control the magnitude of ankle plantarflexion. This meant ankle plantarflexion did not directly

218

influence impact efficiency, rather, ankle motion was a passive response to the initial conditions

of impact.

Foot-ball impact characteristics influenced kicking accuracy. Prior to this thesis, little was

known about how foot-ball impact influenced ball flight characteristics and kicking accuracy. The

second aim of this thesis was to identify how foot-ball impact characteristics influenced ball flight

characteristics and kicking accuracy. The relationship between foot-ball impact and ball flight

characteristics was explored with both a mechanical kicking machine (via systematic exploration)

and by performing an intra-individual analysis of human kickers. The oblique impact theory

applied to the duration of impact provided a theoretical explanation linking foot-ball impact and

ball flight characteristics. Subsequent analysis of ball flight characteristics and a measurement of

kicking accuracy identified that ball flight characteristics influenced kicking accuracy. From these

results, it was concluded foot-ball impact characteristics influence kicking accuracy. Between the

execution of kicks, players varied their impact characteristics. This variability can be functional,

as players must vary their impact characteristics to satisfy different task constraints. This

variability can also be non-functional. More consistent performance of the singular task, where

the task constraints were held constant, was obtained by players reducing the magnitude of

variability in their impact characteristics. Because the impact phase was extremely short (~10-12

ms), players were unable to receive feedback from the initial conditions of impact and make

corrective changes. Inaccurate kicks were due to players using an incorrect combination of impact

characteristics, such as impacting the far lateral or medial sides of the ball when kicking toward

a target that was positioned straight ahead.

In conclusion, this thesis identified foot-ball impact characteristics influenced impact

efficiency, ankle motion, ball flight characteristics, and kicking accuracy. These results have

practical implications for the improve of kicking performance. Maintaining a firm ankle, a

commonly used coaching cue, and other coaching cues, were discussed throughout the thesis. The

methods used within this study, of a mechanical kicking machine and subsequent human testing,

were successful in avoiding the issue of confounding impact characteristics. Several areas of

219

future research were identified. Most notable, several strategies involving interventions were

identified as potentially effective at improving kicking performance. However, future work is

required to determine the effectiveness of these interventions. Future work exploring foot-ball

impact should also employ methods that remove the likelihood of confounding impact

characteristics, such as an intra-individual analysis where individual differences in the physical

size, shape and technique of the performers will be eliminated.

220

Chapter 12: References

Alam, F., Subic, A., Watkins, S., & Smits, A. J. (2009). Aerodynamics of an Australian rules foot

ball and rugby ball. In M. Peters (Ed.), Computational Fluid Dynamics for Sport

Simulation (Vol. 72, pp. 103-127): Springer, Berlin, Heidelberg.

Amos, M., & Morag, E. (2002). Effect of shoe mass on soccer kicking velocity. In Proceedings

CD IV World Congress of Biomechanics Calgary.

Andersen, T. B., Dörge, H. C., & Thomsen, F. I. (1999). Collisions in soccer kicking. Sports

Engineering, 2, 121-125.

Andersen, T. B., Kristensen, L. B., & Sorensen, H. (2005). Coefficient of Restitution (COR) in

Toe and Instep Soccer Kicks. In Science and Football. London: Routledge.

Andersen, T. B., Kristensen, L. B., & Sorensen, H. (2008). Biomechanical Differences Between

Toe and Instep Kicking; Influence of Contact Area on the Coefficient of Restitution.

Football Science, 5, 45-50.

Arutyunyan, G., Gurfinkel, V., & Mirskii, M. (1968). Investigation of aiming at a target.

Biophysics, 13, 642-645.

Asai, T., Carré, M., Akatsuka, T., & Haake, S. (2002). The curve kick of a football I: impact with

the foot. Sports Engineering, 5, 183-192.

Asami, T., & Nolte, V. (1983). Analysis of powerful ball kicking. Biomechanics VIII-B, 4, 965-

970.

Atack, A., Trewartha, G., & Bezodis, N. (2015). Development and evaluation of a method to

quantify rugby place kick performance from initial ball flight data. In F. Colloud, M.

Domalain & T. Monnet (Eds.), 33rd International Conference of Biomechanics in Sports

(Vol. 33). Poitiers, France.

Atack, A., Trewartha, G., & Bezodis, N. (2017). The Differences in Rugby Place Kick Technique

Between Successful and Less Successful Kickers In W. Potthast, A. Niehoff & S. David

(Eds.), 35th International Conference on Biomechanics in Sports. German Sport

University Cologne, Cologne, Germany.

Ball, K. (2008a). Biomechanical considerations of distance kicking in Australian Rules football.

Sports Biomechanics, 7, 10-23.

Ball, K. (2008b). Foot interaction during kicking in Australian Rules football. In T. Reilly & F.

Korkusuz (Eds.), Science and Football VI: The Proceedings of the Sixth World Congress

on Science and Football (Vol. VI, pp. 36-40). Milton Park: Routledge.

Ball, K. (2010). Kick impact characteristics for different Rugby League kicks. In R. Jensen, W.

Ebben, E. Petushek, C. Richter & K. Roemer (Eds.), 28th International Conference on

Biomechanics in Sports (Vol. 28). Marquette: Michigan State University.

Ball, K. (2011). Kinematic comparison of the preferred and non-preferred foot punt kick. Journal

of Sports Sciences, 29, 1545-1552.

221

Ball, K., Ingleton, C., Peacock, J., & Nunome, H. (2013). Ball impact dynamics in the punt kick.

In T. Y. Shiang, W.-H. Ho, P. C. Huang & C.-L. Tsai (Eds.), 31st International

Conference on Biomechanics in Sports. Taipei.

Ball, K., Smith, J., & MacMahon, C. (2010). Kick impact characteristics of junior kickers. In R.

Jensen, W. Ebben, E. Petushek, C. Richter & K. Roemer (Eds.), 28th International

Conference on Biomechanics in Sports (Vol. 28). Marquette: Michigan State University.

Bartlett, R., Wheat, J., & Robins, M. (2007). Is movement variability important for sports

biomechanists? Sports Biomechanics, 6, 224-243.

Betzler, N. F., Monk, S. A., Wallace, E. S., & Otto, S. R. (2012). Variability in clubhead

presentation characteristics and ball impact location for golfers' drives. Journal of Sports

Sciences, 30, 439-448.

Betzler, N. F., Monk, S. A., Wallace, E. S., & Otto, S. R. (2014). The relationships between driver

clubhead presentation characteristics, ball launch conditions and golf shot outcomes.

Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports

Engineering and Technology, 228, 242-249.

Bower, R. (2012). The sweet spot of a cricket bat for low speed impacts. Sports Engineering, 15,

53-60.

Brody, H. (1981). Physics of the tennis racket II: The "sweet spot". American Journal of Physics,

49, 816-819.

Carré, M. J., Asai, T., Akatsuka, T., & Haake, S. J. (2002). The curve kick of a football II: flight

through the air. Sports Engineering, 5, 193-200.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences: Lawrence Erlbaum.

Cross, R. (1998). The sweet spot of a baseball bat. American Journal of Physics, 66, 772-779.

Cross, R. (1999). The bounce of a ball. American Journal of Physics, 67, 222-227.

Cross, R. (2011). Physics of Baseball & Softball. New York Dordrecht Heidelberg London:

Springer.

Cross, R. (2013). Impact of sports balls with striking implements. Sports Engineering, 17, 3-22.

Davids, K. W. (2010). The constraints-based approach to motor learning: Implications for a non-

linear pedagogy in sport and physical education. In Motor learning in practice: A

constraints-led approach (pp. 3-16): Routledge (Taylor & Francis Group).

De Witt, J. K., & Hinrichs, R. N. (2012). Mechanical factors associated with the development of

high ball velocity during an instep soccer kick. Sports Biomechanics, 11, 382-390.

Dichiera, A., Webster, K., Kuilboer, L., Morris, M., Bach, T., & Feller, J. (2006). Kinematic

patterns associated with accuracy of the drop punt kick in Australian Football. Journal of

Science and Medicine in Sport, 9, 292-298.

Dickinson, M. H., Farley, C. T., Full, R. J., Koehl, M. A. R., Kram, R., & Lehman, S. (2000).

How Animals Move: An Integrative View. Science, 288, 100.

Djamovski, V., Rosette, P., Chowdhury, H., Alam, F., & Steiner, T. (2012). A comparative study

of rugby ball aerodynamics. Procedia Engineering, 34, 74-79.

222

Dørge, H. C., Andersen, T. B., Sørensen, H., & Simonsen, E. B. (2002). Biomechanical

differences in soccer kicking with the preferred and the non-preferred leg. Journal of

Sports Sciences, 20, 293-299.

Flemmer, L. C., & Flemmer, C. R. (2015). A comparison of kicking accuracy for elite rugby

players and a robotic kicker. International Journal of Performance Analysis in Sport, 15,

112-124.

Ford, S., & Sayers, M. (2015). Lower limb movement variability during rugby union place

kicking. In F. Colloud, M. Domalain & T. Monnet (Eds.), International Conference of

Biomechanics in Sports (Vol. 33). Poitiers, France.

Fraser, S., Harland, A., Donovan, P., & O'Shea, L. (2012). Development of an end-effector to

simulate the foot to ball interaction of an instep kick in soccer. Procedia Engineering, 34,

284-289.

Ghasemi, A., & Zahediasl, S. (2012). Normality Tests for Statistical Analysis: A Guide for Non-

Statisticians. International Journal of Endocrinology and Metabolism, 10, 486-489.

Glazier, P., Reid, M., & Ball, K. (2015). Expertise in the performance of multi-articular sports

actions. In J. Baker & D. Farrow (Eds.), Routledge Handbook of Sport Expertise (pp. 84-

94): Taylor and Francis.

Goff, J. E. (2013). A review of recent research into aerodynamics of sport projectiles. Sports

Engineering, 16, 137-154.

Hayes, J. G. (1970). Numerical approximation to functions and data. University of London: The

Athlone Press.

Hennig, E. M. (2011). The influence of soccer shoe design on player performance and injuries.

Research in Sports Medicine, 19, 186-201.

Hennig, E. M. (2014). Plantar pressure measurements for the evaluation of shoe comfort, overuse

injuries and performance in soccer. Footwear Science, 6, 119-127.

Hennig, E. M., & Althoff, K. (2013). Soccer Shoe Design and Its Influence on Player's

Performance. In R. S. Goonetilleke (Ed.), The Science of Footwear (pp. 561-577). Boca

Raton: CRC Press.

Hennig, E. M., & Althoff, K. (2018). Kicking accuracy can be influenced by soccer shoe design.

In H. Nunome, E. Hennig & N. Smith (Eds.), Football Biomechanics (3 ed.). London and

New York: Routledge.

Hennig, E. M., Althoff, K., & Hoemme, A.-K. (2009). Soccer footwear and ball kicking accuracy.

Footwear Science, 1, 85-87.

Hennig, E. M., & Sterzing, T. (2010). The influence of soccer shoe design on playing

performance: a series of biomechanical studies. Footwear Science, 2, 3-11.

Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian journal

of statistics, 6, 65-70.

Holmes, C. (2008). Advanced modelling of ovoid balls. Loughborough University.

223

Holmes, C., Jones, R., Harland, A., & Petzing, J. (2006). Ball launch characteristics for elite rugby

union players. In The Engineering of Sport 6 (pp. 211-216): Springer.

Iga, T., Nunome, H., Inoue, K., & Ikegami, Y. (2013). Basic mechanical analysis of soccer ball

impact. In T. Y. Shiang, W.-H. Ho, P. C. Huang & C.-L. Tsai (Eds.), 31 International

Conference on Biomechanics in Sports (Vol. 31). Taipei, Taiwan.

Iga, T., Nunome, H., Sano, S., Sato, N., & Ikegami, Y. (2017). Novel mathematical model to

estimate ball impact force in soccer. Sports Biomechanics.

Ishii, H., Yanagiya, T., Naito, H., Katamoto, S., & Maruyama, T. (2009). Numerical study of ball

behavior in side-foot soccer kick based on impact dynamic theory. Journal of

Biomechanics, 42, 2712-2720.

Ishii, H., Yanagiya, T., Naito, H., Katamoto, S., & Maruyama, T. (2012). Theoretical study of

factors affecting ball velocity in instep soccer kicking. Journal of Applied Biomechanics,

28, 258-270.

Kellis, E., & Katis, A. (2007). Biomechanical characteristics and determinants of instep soccer

kick. Journal of Sports Science and Medicine, 6, 154-165.

Koike, S., & Bezodis, N. (2017). Determining the dynamic contributions to kicking foot speed in

rugby place kicking. In W. Potthast, A. Niehoff & S. David (Eds.), 35th International

Conference on Biomechanics in Sports (Vol. 35, pp. 167).

Kubo, K., Kanehisa, H., & Fukunaga, T. (2002). Effects of resistance and stretching training

programmes on the viscoelastic properties of human tendon structures in vivo. The

Journal of Physiology, 538, 219-226.

Latash, M. L. (2012). Fundamentals of Motor Control (1st ed.). London, UK: Academic Press.

Lees, A., Asai, T., Andersen, T. B., Nunome, H., & Sterzing, T. (2010). The biomechanics of

kicking in soccer: a review. Journal of Sports Sciences, 28, 805-817.

Lees, A., & Nolan, L. (1998). The biomechanics of soccer: a review. Journal of Sports Sciences,

16, 211-234.

Morris, J., Sayers, M., & Stuelcken, M. (2016). Movement variability in rugby union punt

kicking. In M. Ae, Y. Enomoto, N. Fujii & H. Takagi (Eds.), 34th International

Conference on Biomechanics in Sports (Vol. 34). Tsukuba, Japan.

Morse, C. I., Degens, H., Seynnes, O. R., Maganaris, C. N., & Jones, D. A. (2008). The acute

effect of stretching on the passive stiffness of the human gastrocnemius muscle tendon

unit. The Journal of Physiology, 586, 97-106.

Moschini, A., & Smith, N. (2012). Effect of shoe mass on soccer kicking velocity. In E. J.

Bradshaw, A. Burnett & P. Hume (Eds.), 30th International Conference on Biomechanics

in Sports (Vol. 30). Melbourne, Australia.

Nunome, H., Asai, T., Ikegami, Y., & Sakurai, S. (2002). Three-dimensional kinetic analysis of

side-foot and instep soccer kicks. Med Sci Sports Exerc, 34, 2028-2036.

Nunome, H., Ball, K., & Shinkai, H. (2014). Myth and fact of ball impact dynamics in football

codes. Footwear Science, 6, 105-118.

224

Nunome, H., Ikegami, Y., Kozakai, R., Apriantono, T., & Sano, S. (2006a). Segmental dynamics

of soccer instep kicking with the preferred and non-preferred leg. Journal of Sports

Sciences, 24, 529-541.

Nunome, H., Lake, M., Georgakis, A., & Stergioulas, L. K. (2006b). Impact phase kinematics of

instep kicking in soccer. Journal of Sports Sciences, 24, 11-22.

Peacock, J. (2013). Comparisons of foot to ball interaction in Australian Football in elite males.

Unpublished Honours, Victoria University.

Peacock, J., & Ball, K. (2016). The impact phase of drop punt kicking: validation and

experimental data of a mechanical kicking limb In M. Ae, Y. Enomoto, N. Fujii & H.

Takagi (Eds.), 34th International Conference on Biomechanics in Sports (Vol. 34).

Tsukuba, Japan.

Peacock, J., & Ball, K. (2017). The relationship between foot-ball impact and flight characteristics

in punt kicking. Sports Engineering, 20, 221-230.

Peacock, J., & Ball, K. (2018a). The influence of joint rigidity on impact efficiency and ball

velocity in football kicking. Journal of Biomechanics, 71, 245-250.

Peacock, J., & Ball, K. (2018b). Strategies to improve impact efficiency in football kicking. Sports

Biomechanics.

Peacock, J., Ball, K., & Taylor, S. (2017a). The impact phase of drop punt kicking for maximal

distance and accuracy. Journal of Sports Sciences, 35, 2289-2296.

Peacock, J., Ball, K., & Taylor, S. (2017b). The relationship between impact and ball flight

characteristics in football kicking: Intra-individual analysis of ankle motion during

impact. In ISB 2017 Congress XXVI. Brisbane, Australia.

Phillips, E., Portus, M., Davids, K., & Renshaw, I. (2012). Performance accuracy and functional

variability in elite and developing fast bowlers. Journal of Science and Medicine in Sport,

15, 182-188.

Plagenhoef, S. (1971). Patterns of human motion: A cinematographic analysis: Prentice-Hall

Englewood Cliffs, NJ.

Roberts, J. R., Jones, R., & Rothberg, S. (2001). Measurement of contact time in short duration

sports ball impacts: an experimental method and correlation with the perceptions of elite

golfers. Sports Engineering, 4, 191-203.

Robins, M., Davids, K., Bartlett, R., & Wheat, J. S. (2008). Changes in compensatory variability

as a function of task expertise and distance during basketball shooting. In Y.-H. Kwon, J.

Shim, J. K. Shim & I.-S. Shin (Eds.), 26th International Conference on Biomechanics in

Sports (pp. 473-476). Seoul, Korea.

Sayers, M., & Morris, J. (2012). Three dimensional pelvis and hip interaction during punt kicking:

skilled versus novice players. In E. J. Bradshaw, A. Burnett & P. Hume (Eds.), 30th

International Conference on Biomechanics in Sports (Vol. 30). Melbourne, Australia.

Shinkai, H., Nunome, H., Isokawa, M., & Ikegami, Y. (2009). Ball Impact Dynamics of Instep

Soccer Kicking. Medicine & Science in Sports & Exercise, 41, 889-897.

225

Shinkai, H., Nunome, H., Suito, H., Inoue, K., & Ikegami, Y. (2013). Cross-sectional change of

ball impact in instep kicks from junior to professional footballers. In H. Nunome, B. Drust

& B. Dawson (Eds.), Science and Football VII. London: Taylor and Francis.

Sinkjaer, T., Toft, E., Andreassen, S., & Hornemann, B. C. (1988). Muscle stiffness in human

ankle dorsiflexors: intrinsic and reflex components. Journal of neurophysiology, 60,

1110-1121.

Smith, J., Ball, K., & MacMahon, C. (2009). Foot-to-ball interaction in preferred and non-

preferred leg australian rules kicking. In A. Harrison, R. Anderson & I. Kenny (Eds.),

27th International Conference on Biomechanics in Sports (Vol. 27). Limerick, Ireland.

Sterzing, T., & Hennig, E. M. (2008). The influence of soccer shoes on kicking velocity in full-

instep kicks. Exercise and Sport Sciences Reviews, 36, 91-97.

Sterzing, T., Kroiher, J., & Hennig, E. (2009). Kicking velocity: Barefoot kicking superior to shod

kicking? In T. Reilly & F. Korkusuz (Eds.), Science and football VI. London, United

Kingdom: Routledge.

Tabachnick, B. G., & Fidell, L. S. (2001). Using multivariate statistics (4th ed.). Needham

Heights, Massuchusets: Allyn and Bacon.

Taylor, D. C., Dalton JR, J. D., Seaber, A. V., & Garrett JR, W. E. (1990). Viscoelastic properties

of muscle-tendon units: the biomechanical effects of stretching. The American Journal of

Sports Medicine, 18, 300-309.

Tol, J. L., Slim, E., van Soest, A. J., & van Dijk, C. N. (2002). The relationship of the kicking

action in soccer and anterior ankle impingement syndrome: a biomechanical analysis. The

American Journal of Sports Medicine, 30, 45-50.

Tsaousidis, N., & Zatsiorsky, V. (1996). Two types of ball-effector interaction and their relative

contribution to soccer kicking. Human Movement Science, 15, 861-876.

Williams, C. D., Regnier, M., & Daniel, T. L. (2012). Elastic Energy Storage and Radial Forces

in the Myofilament Lattice Depend on Sarcomere Length. PLoS Computational Biology,

8, e1002770.

Winter, D. A. (1990). Biomechanics and motor control of human movement: John Wiley & Sons.

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Appendix B: Published manuscript of Study 2

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Documents

The relationship between foot-ball impact with kick outcome